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+1 vote
3.8k views
in Mathematics by (67.9k points)

The circle x+ y– 2x – 6y + 2 = 0 intersects the parabola y2 = 8x orthogonally at the point P. The equation of the tangent to the parabola at P can be

(a)  2x – y + 1 = 0

(b)  2x + y – 2 = 0

(c)  x + y – 4 = 0

(d) x  – y – 4 = 0

1 Answer

+2 votes
by (63.3k points)
selected by
 
Best answer

Correct option  (a) 2x –y+1 = 0

Explanation:

 Let y = mx + 2/m be tangent to y2 = 8x. Since circle intersects the parabola orthogonally. So this tangent is the normal for the circle. Every normal of the circle passes through its centre. So centre (1, 3).

3 - m + 2/m2 - 3m + 2 = 0
(m - 2)(m -1) = 0
m = 1, 2
y = x + 2 or y = 2x + 1

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