Question

Find the equations of the chords of the parabola $y^2=4ax$ which pass through the point (-6a,0)and which subtends an angle of ${45}^{\circ }$ at the vertex.

Answer 1

We have,

Equation of parabola $y^2=4ax$

Point $(x_1,y_1)=(-6a,0)$

Angle is ${45}^o$

Slope

$m=\tan \theta =\tan {45}^o$

$m=1$

We know that,

$y-y_1=m(x-x_1)$

$\Rightarrow y-0=1(x+6a)$

$\Rightarrow y=x+6a$

$\Rightarrow x-y+6a=0$

Hence, this is the answer.