Two parabolas have the same focus (4 ,3 ) and their directrices are the x-axis and the y-axis, respectively. If these parabolas intersects at the points A and B, then ( AB )^2 is equal to:

Question

Accepted Answer

Correct answer: C. (c) The parabolas are (x-4 )^2+ (y-3 )^2=x^2 … (i) and (x-4 )^2+ (y-3 )^2=y^2 … If point of intersection are A (x_1 ,y_1 ) and B (x_2 ,y_2 ) By solving (i) and (ii), we get x_1+x_2=14 and x_1x_2=25 ( AB )^2=2((x_1+x_2)^2-4x_1x_2)=192

$Two parabolas have the same focus (4, 3) and their directrices are the x -axis and the y -axis, respectively. If these parabolas intersects at the points A and B, then (AB)^{2} is equal to:$

Solution

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