Question

the equation of image of the curve ay2=x3 wrt to the line x+y=a

Answer 1

Explanation:

let the equation of the line is $a_1x+b_1y+c=0$ and the image of the point p $(x_1,y_1)$ is Q$(x_2,y_2)$ is given by

$\frac{x_2-x_1}{a_1}=\frac{y_2-y_1}{b_1}=\frac{2(a_1x_1+b_1y_1+c)}{a_1^2+b_1^2}$

Given equation is ay² = x³

Three points on the curve are (0,0 ), (a,a) and (a,-a)

then

image of the point (0,0) with respect to the line x+y=a is (a,a)

similarly

image of the point  (a,a)  with respect to the line x+y=a is (0,0)

image of the point  (a,-a)  with respect to the line x+y=a is (2a,0)

now , the three points lying on the image curve is (a,a) , (0,0) and (2a,a)

now , plot these points in the equation curve passing through the point

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