Let the lines y - 2 = m 1 x - 5 and y + 4 = m 2 x - 3 intersect at right angles at P (where m 1 and m 2 are parameters). If locus of P is x 2 + y 2 + g x + f y + 7 = 0 , then g 2 2 + f 2 2 - 7 is equal to

Question

Let the lines y - 2 = m 1 x - 5 and y + 4 = m 2 x - 3 intersect at right angles at P (where m 1 and m 2 are parameters). If locus of P is x 2 + y 2 + g x + f y + 7 = 0 , then g 2 2 + f 2 2 - 7 is equal to, 1, 2, 8, 10

MARKS App · Accepted Answer

Since the lines intersect at right angle, therefore, the locus of the point of intersection of lines is a circle with end points of diameter as 5 , 2 & 3 , - 4 x - 5 x - 3 + y - 2 y + 4 = 0 ⇒ x 2 + y 2 - 8 x + 2 y + 7 = 0 Hence, g 2 2 + f 2 2 - 7 = 16 + 1 - 7 = 10

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