Question

if a circle cuts a parabola at the points P, Q, R, S show that PQ and RS are equally inclined to the axes.​

Answer 1

the circle is of the form: x

2

+y

2

+2gx+2fy+c=0

the parabola is of the form: y

2

=4ax

as the circle and parabola intersect at four points and any point on the parabola is of the form (at

2

,2at)

let the point (at

2

,2at) lies on the circle and we get

a

2

t

4

+t

2

(4a

2

+2ag)+4aft+c=0

since sum of the roots is equal to zero

i.e. t

1

+t

2

+t

3

+t

4

=0

the sum of the ordinates of the points

the slope of two pair of points, let's say points

similarly, the slope of other two pair of points

as a result, we get 1

= 0 , which was proved earlier.

thus, the lines are equally inclined to the axis.

Answer 2

Answer:

thanks for free points