circles - c1 Watch

longsightdon
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#1
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Hi guys wondering if someone could help me with these?

1. the points p and q have coordinates (-2, 6) and (4, -1) respectively. given that PQ is a diameter of a circle C,

i) find the cooridnates of the circle
ii)show that C has the equation x^2+ y^2-2x-5y-14=0

the point R has coordinates (2, 7)

iii) show that R lies on C and hence state the size of angle PRQ in degrees

2. the circle C has the equation x^2+y^2 +10x -8y+k=0, where k is the constant, given that the point with coordinates (-6,5) lies on C

i) find the value of k
ii) find the coordinates of the centre and the radius of C

A straight line which passes through the point A (2,3) is a tangent to C at the point B
iii)find the length AB in the form k square root 3
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davros
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(Original post by longsightdon)
Hi guys wondering if someone could help me with these?

1. the points p and q have coordinates (-2, 6) and (4, -1) respectively. given that PQ is a diameter of a circle C,

i) find the cooridnates of the circle
ii)show that C has the equation x^2+ y^2-2x-5y-14=0

the point R has coordinates (2, 7)

iii) show that R lies on C and hence state the size of angle PRQ in degrees

2. the circle C has the equation x^2+y^2 +10x -8y+k=0, where k is the constant, given that the point with coordinates (-6,5) lies on C

i) find the value of k
ii) find the coordinates of the centre and the radius of C

A straight line which passes through the point A (2,3) is a tangent to C at the point B
iii)find the length AB in the form k square root 3
For 1)i, if PQ is a diameter then its midpoint is the centre. Can you proceed from here?
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TeeEm
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(Original post by longsightdon)
Hi guys wondering if someone could help me with these?

1. the points p and q have coordinates (-2, 6) and (4, -1) respectively. given that PQ is a diameter of a circle C,

i) find the cooridnates of the circle
ii)show that C has the equation x^2+ y^2-2x-5y-14=0

the point R has coordinates (2, 7)

iii) show that R lies on C and hence state the size of angle PRQ in degrees

2. the circle C has the equation x^2+y^2 +10x -8y+k=0, where k is the constant, given that the point with coordinates (-6,5) lies on C

i) find the value of k
ii) find the coordinates of the centre and the radius of C

A straight line which passes through the point A (2,3) is a tangent to C at the point B
iii)find the length AB in the form k square root 3
Have you done any parts from these questions?
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longsightdon
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(Original post by davros)
For 1)i, if PQ is a diameter then its midpoint is the centre. Can you proceed from here?
i got (1, 5/2) but im not sure if ive done it right

(Original post by TeeEm)
Have you done any parts from these questions?
the only one i can do 1 i) but dunno if i got it right
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davros
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(Original post by longsightdon)
i got (1, 5/2) but im not sure if ive done it right



the only one i can do 1 i) but dunno if i got it right
If that is the centre then work out the radius from one of the points you're given then plug everything into the standard equation for a circle and simplify.
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longsightdon
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(Original post by davros)
If that is the centre then work out the radius from one of the points you're given then plug everything into the standard equation for a circle and simplify.
how do i do that
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davros
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(Original post by longsightdon)
how do i do that
Do what?

Can you work out the radius?

Do you know what the standard equation of a circle is?

Where are you getting stuck exactly?
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