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if y=m1x+c and y=m2x+c are two tangents to the parabola y^2+4a(x+a)=0 then, find the relation between m1 and m2 a)m1+m2=0 b)1+m1+m2=0 c)m1m2-1=0 ​d)1+m1m2=0 please answer with solution

if y=m1x+c and y=m2x+c are two tangents to the parabola y^2+4a(x+a)=0
then, find the relation between m1 and m2
a)m1+m2=0
b)1+m1+m2=0
c)m1m2-1=0
​d)1+m1m2=0
please answer with solution

Grade:11

1 Answers

Deepak Kumar Shringi
askIITians Faculty 4404 Points
5 years ago
let line y=mx+c is tangent then
(mx+c)2+4ax+4a2=0 here D=0 as it is tangent then
m2x2+2mxc+c2+4ax+4a2=0
D=0
(2mc+4a)2-4(c2+4a2)m2=0
16a2+16amc-16a2m2=0
a+mc=am2
c=a(m2-1)/m replace it again
for both tangents c is same so m1m2 =1

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