AP EAMCET Engineering 20 Apr 2019 Shift 1 Paper

The equation of the normal that have slope m to the parabola
y2=4ax is
y=mx−2am−am3
It passes through (h,k) then
k=mh−2am−am3

Let the roots be m1,m2,m3 so,
m1m2m3=−‌

k

a

And
m1m2=−1
So
m3=‌

k

a

Then
k‌‌=‌

k

a

h−2a‌

k

a

−a(‌

k

a

)3
1‌‌=‌

h

a

−2−‌

k2

a2

‌

k2

a2

‌‌=‌

h

a

−3
k2‌‌=a(h−3a)
By taking locus of (h,k)
y2−ax+3a2=0