Question

The point of intersection of tangents at the points on the parabola $y^2=4x$ whose ordinates are $4$ and $6$ is

• A. $(6,5)$
• B. $(7,3)$
• C. $(9,10)$
• D. $(6,10)$

Answer 1

The correct option is A $(6,5)$

The point of intersection of tangents at any two points $A(a{t}_1{}^2,2a{t}_1)\text{and}B(a{t}_2^2,2a{t}_2)$ on the parabola $y^2=4ax$ is given by $(a{t}_1{t}_2,a(t_1+t_2\left)\right)$
$2a{t}_1=4,2a{t}_2=6$
For the parabola $y^2=4x$
$\Rightarrow a=1\Rightarrow t_1=2,t_2=3$
Then point of intersection of tangents is $(1\times 2\times 3,1\times (2+3\left)\right)=(6,5)$