Question

Find equation of locus of p if the line segment joining (2,3)and(-1,5)subtends a right angle at p

Answer 1

We have to find the locus of a point P if the line segment joining points (2 , 3) and (-1, 5) subtends a right angle at P.

solution : let point P is (h, k).

a line segment formed by joining the points A(2, 3) and B(-1,5) subtends a right angle at P.

so slope of line PA × slope of line PB = -1

⇒(k - 3)/(h - 2) × (k - 5)/(h + 1) = -1

⇒(k - 3)(k - 5) + (h - 2)(h + 1) = 0

⇒k² - (3 + 5)k + 15 + h² -(2 - 1)h - 2 = 0

⇒k² - 8k + 15 + h² - h - 2 = 0

⇒h² + k² - 8k - h + 13 = 0

now putting h = x and k = y

so x² + y² - x - 8y + 13 = 0

Therefore the locus of the point P is x² + y² - x - 8y + 13.

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the locus of point P such that segment

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Answer 2

Answer:

$\\ \ \ \\ {x}^{2} +{y}^{2} - x - 8y + 13 = 0$