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The curves x^(2) +y^(2) +6x - 24y +72 = ...

The curves `x^(2) +y^(2) +6x - 24y +72 = 0` and `x^(2) - y^(2) +6x +16y - 46 = 0` intersect in four points P,Q,R and S lying on a parabola. Let A be the focus of the parabola, then

A

`AP + AQ +AR +AS = 20`

B

`AP + AQ +AR +AS = 40`

C

vertex of the parabola is at `(-3,1)`

D

coordinates of A are `(-3,1)`

Text Solution

Verified by Experts

The correct Answer is:
B, C
The points of intersection P,Q,R,S lie on
`2x^(2) +12x -8y +26 =0` (by adding equations)
i.e., `(x+3)^(2) =4(y-1)`
So, vertex is `(-3,1)` and focus is `(-3,2)`.
Points of intersection also lie on `y^(2) - 20y +59 =0`. (by substracting equations)
`:.` Sum of two of the ordinates `= 20`
`:. AP + AQ + AR + AS = 40`
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