HELP PLZ!!!! MEI core 1 coordinate geometry section 2: curves and circles Q10
10) the liney=2x+3 is a tangent to a circle with a centre (2,-3)
the radius of the circle is ??
am i ment to use the quadratic formulae i tried that but calculator comes up with error
i got 5x^2+8x+22=r^2
a=5 b=8 c=22 is that wrong?
the radius of the circle is ??
am i ment to use the quadratic formulae i tried that but calculator comes up with error
i got 5x^2+8x+22=r^2
a=5 b=8 c=22 is that wrong?
Original post by Need-Help-Quick
10) the liney=2x+3 is a tangent to a circle with a centre (2,-3)
the radius of the circle is ??
am i ment to use the quadratic formulae i tried that but calculator comes up with error
i got 5x^2+8x+22=r^2
a=5 b=8 c=22 is that wrong?
the radius of the circle is ??
am i ment to use the quadratic formulae i tried that but calculator comes up with error
i got 5x^2+8x+22=r^2
a=5 b=8 c=22 is that wrong?
where does this quadratic come from?
Original post by the bear
you write
( x - 2 )2 + ( y + 3 )2 - r2 = 0
then substitute 2x + 3 for y
which makes a quadratic equation. then think about the Discriminant if the line is a tangent....
( x - 2 )2 + ( y + 3 )2 - r2 = 0
then substitute 2x + 3 for y
which makes a quadratic equation. then think about the Discriminant if the line is a tangent....
oh ok
so do i use b^2-4ac?? im confused what you mean sorry im bad at english
Original post by Need-Help-Quick
10) the liney=2x+3 is a tangent to a circle with a centre (2,-3)
the radius of the circle is ??
am i ment to use the quadratic formulae i tried that but calculator comes up with error
i got 5x^2+8x+22=r^2
a=5 b=8 c=22 is that wrong?
the radius of the circle is ??
am i ment to use the quadratic formulae i tried that but calculator comes up with error
i got 5x^2+8x+22=r^2
a=5 b=8 c=22 is that wrong?
Find equation of line through (2,-3) perpendicular to y=2x+3.
Find where these two lines intersect
then find distance of this point from (2,-3)
no need for any quadratics.
Original post by the bear
you write
( x - 2 )2 + ( y + 3 )2 - r2 = 0
then substitute 2x + 3 for y
which makes a quadratic equation. then think about the Discriminant if the line is a tangent....
( x - 2 )2 + ( y + 3 )2 - r2 = 0
then substitute 2x + 3 for y
which makes a quadratic equation. then think about the Discriminant if the line is a tangent....
Original post by Need-Help-Quick
so do i use b^2-4ac?? im confused what you mean sorry im bad at english
consider an alternative method after you draw a diagram
find the gradient of the tangent
work out the equation of a perpendicular line which passes through the centre
find where these 2 lines meet
Find the distance from that point to the centre.
This is the radius
is this any good?
Original post by TeeEm
consider an alternative method after you draw a diagram
find the gradient of the tangent
work out the equation of a perpendicular line which passes through the centre
find where these 2 lines meet
Find the distance from that point to the centre.
This is the radius
is this any good?
find the gradient of the tangent
work out the equation of a perpendicular line which passes through the centre
find where these 2 lines meet
Find the distance from that point to the centre.
This is the radius
is this any good?
yes that would not involve quadratics...
Original post by TeeEm
consider an alternative method after you draw a diagram
find the gradient of the tangent
work out the equation of a perpendicular line which passes through the centre
find where these 2 lines meet
Find the distance from that point to the centre.
This is the radius
is this any good?
find the gradient of the tangent
work out the equation of a perpendicular line which passes through the centre
find where these 2 lines meet
Find the distance from that point to the centre.
This is the radius
is this any good?
how do i find gradient of tangent?
Original post by Need-Help-Quick
how do i find gradient of tangent?
I thought y=2x-3 was a tangent.
Original post by TeeEm
I thought y=2x-3 was a tangent.
thats what i thought it was but you said to find the tangent which got me confused
Original post by Need-Help-Quick
thats what i thought it was but you said to find the tangent which got me confused
I gave a general method, so I said find the gradient of the tangent.
However I fully understand the confusion as it hardly involves any calculation, just merely stating that it is 2
i dont understand one bit of it can you give me an example if thats ok?
Original post by Need-Help-Quick
i dont understand one bit of it can you give me an example if thats ok?
are you referring to my method/approach?
yea
is the perpendicular of the gradient -3?
is the perpendicular of the gradient -3?
Original post by Need-Help-Quick
yea
is the perpendicular of the gradient -3?
is the perpendicular of the gradient -3?
I am attaching a very similar question from my own bank of questions.
PDF.pdf
enlarge solution in the bottom right.
see if this helps.
centre (2,-3)
(x-2)^2+(y+3)^2=r^2
y=2x+3
y--3=2x-4
y=2x-7
2x-7=2x+3
this right?????
(x-2)^2+(y+3)^2=r^2
y=2x+3
y--3=2x-4
y=2x-7
2x-7=2x+3
this right?????
1) find equation of circle
2) sub in for y
3) its a tangent to the roots will be equal, think of the tangent as the x-axis and the circle as an x^2 curve if you have to
4)if the roots are equal then the discriminant must =0
5) solve the discriminant equation to give something that looks like:
20^2 - 20*40 + 20r^2 = 0
solve
SPOILERZZZZ:
ans is root(20) if you want to check at the end
2) sub in for y
3) its a tangent to the roots will be equal, think of the tangent as the x-axis and the circle as an x^2 curve if you have to
4)if the roots are equal then the discriminant must =0
5) solve the discriminant equation to give something that looks like:
20^2 - 20*40 + 20r^2 = 0
solve
SPOILERZZZZ:
ans is root(20) if you want to check at the end
Original post by Modafinil Fanta
1) find equation of circle
2) sub in for y
3) its a tangent to the roots will be equal, think of the tangent as the x-axis and the circle as an x^2 curve if you have to
4)if the roots are equal then the discriminant must =0
5) solve the discriminant equation to give something that looks like:
20^2 - 20*40 + 20r^2 = 0
solve
SPOILERZZZZ:
ans is root(20) if you want to check at the end
2) sub in for y
3) its a tangent to the roots will be equal, think of the tangent as the x-axis and the circle as an x^2 curve if you have to
4)if the roots are equal then the discriminant must =0
5) solve the discriminant equation to give something that looks like:
20^2 - 20*40 + 20r^2 = 0
solve
SPOILERZZZZ:
ans is root(20) if you want to check at the end
Hello, the circle is a very convienient distration, and I think examiner intentionally included that into the question in order draw the student's attention and focus towards circle than straight line.
However, you need to know the geometrical fact htat line from centre of circle to the tangent of circle (or for that matter any curve) do always meet at perpendicular direction at the tangential point. In the case of circle, any point on the circumference,
This is a question about finding distance (i.e perpendicular distance) from a point (i.e. a coordinate) to a straight line.
If my memory serves me right, there is a section in cartesian co-ordinate geometry in straightline analysis for finding perpendicular distance from a given point (i.e. coordinates) to a given straight line.
If my memory serves me right, finding the (perpendicular) distance from point P(p,q) to the straight line expressed in the form of ax + by + c = 0.
OR
You can find it from first principles, using the equation straight line (say, L), which is parallel to the given line through P and its intercept.
So, you know the given line's intercept and L's intercept, and draw a perperndicular line from the point where L intercepts Y axis to the given line , and the angle between Y axis and the perpenicular line from the point where L intercepts Y axis to the given line is same as given line's angle with X axis (i.e. given line's gradient). Now you can work out perpendicular distance from the point where L intercepts Y axis to the given line using trignometry.
Hope this helps.
(edited 6 years ago)
Quick Reply
Related discussions
- Maths A Level Coordinate Geometry Question
- A level options
- OCR Further Maths Core Pure 1 25th May 2023
- equations of tangents and normals
- First question from my further maths
- OCR MEI Further Maths Core Pure - 25 May 2023
- Parabola coordinates (FP1) maths help
- AQA A Level Mathematics Paper 1 (7357/1) - 6th June 2023 [Exam Chat]
- Parametrics
- The Directrix of a Parabola
- A level Maths help
- 2022 Edexcel Maths GCSE (Higher) Checklist
- OCR A-level Mathematics A Paper 2 (H240/02) - 13th June 2023 [Exam Chat]
- Can someone please help me on this question I cannot figure out part e
- Coordinate Geometry
- AS further maths - edexcel
- Could someone help me with my A Level Maths homework?
- maths question help
- Further maths: Further Calculus
- OCR A-level Mathematics B (MEI) Paper 1 (H640/01) - 6th June 2023 [Exam Chat]
Latest
Trending
Last reply 4 days ago
Did Cambridge maths students find maths and further maths a level very easy?Last reply 2 weeks ago
Edexcel A Level Mathematics Paper 2 unofficial mark scheme correct me if wrongMaths
71
Trending
Last reply 4 days ago
Did Cambridge maths students find maths and further maths a level very easy?Last reply 2 weeks ago
Edexcel A Level Mathematics Paper 2 unofficial mark scheme correct me if wrongMaths
71
