Quadratics
Consider the curve y=x^2+3x+9
a)there arw two tangents to the curve which go through the origin. Find the equation of each straight line.
B)what are the equations of the two tangents that go through the point (1,2)?
c)are there any points on the coordinate aces which do not have any tangents from the curve going through them?
Mate there any where there is only one tangent? Can you prove it?
Thank you sooooo much. I'm so struggling with these. Hints and tips will be useful too. Well appreciated xx
a)there arw two tangents to the curve which go through the origin. Find the equation of each straight line.
B)what are the equations of the two tangents that go through the point (1,2)?
c)are there any points on the coordinate aces which do not have any tangents from the curve going through them?
Mate there any where there is only one tangent? Can you prove it?
Thank you sooooo much. I'm so struggling with these. Hints and tips will be useful too. Well appreciated xx
Original post by Iwish247
Consider the curve y=x^2+3x+9
a)there arw two tangents to the curve which go through the origin. Find the equation of each straight line.
B)what are the equations of the two tangents that go through the point (1,2)?
c)are there any points on the coordinate aces which do not have any tangents from the curve going through them?
Mate there any where there is only one tangent? Can you prove it?
Thank you sooooo much. I'm so struggling with these. Hints and tips will be useful too. Well appreciated xx
a)there arw two tangents to the curve which go through the origin. Find the equation of each straight line.
B)what are the equations of the two tangents that go through the point (1,2)?
c)are there any points on the coordinate aces which do not have any tangents from the curve going through them?
Mate there any where there is only one tangent? Can you prove it?
Thank you sooooo much. I'm so struggling with these. Hints and tips will be useful too. Well appreciated xx
You need to tell us what you have tried. At least show your partial solution.
1) what kind of straight line equation goes through the origin?
Ans: one like for some gradient m
2) both the quadratic and this line must touch somewhere for there to be a tangent, so we have to equate them:
re-arrange this into a quadratic with x coeffiecient (3-m)
Qn: what, then, do you need for only ONE point of intersection?
(hint: discriminant)
(even though m might turn out to have more than one value, this doesn`t mean the root does)
Ans: one like for some gradient m
2) both the quadratic and this line must touch somewhere for there to be a tangent, so we have to equate them:
re-arrange this into a quadratic with x coeffiecient (3-m)
Qn: what, then, do you need for only ONE point of intersection?
(hint: discriminant)
(even though m might turn out to have more than one value, this doesn`t mean the root does)
(edited 9 years ago)
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