Question

Suppose the circle with equation x 2 + y 2 + 2fx + 2gy + c = 0 cuts the parabola y 2 = 4ax, (a > 0) at four distinct points. If d denotes the sum of ordinates of these four points, then the set of possible values of d is

Answer 1

Answer:

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Answer 2

Answer: {0}

Step-by-step explanation:

We need to find values of y where these two curves intersects.

Substitute y²=4ax in  x²  + y² + 2fx + 2gy + c = 0 i.e substitute x=y²/4ax in x²  + y² + 2fx + 2gy + c = 0.

You will get a degree 4 polynomial and the roots of this polynomial are the ordinates of intersection.

Now finding roots is tedious. Therefore we use Vieta's Theorem.

Part of it states that the sum of roots of polynomial is -(coeff of y³)/(coeff of y^4)

Therefore we get d=0.

Sum of 4 ordinates is zero.