Question

A(1, 3), B(3, 7) & C(7, 15) are three points. P is the midpoint of ABQ is the midpoint of BC. Locus of a point R which satisfies (PR)2 – (QR)= (AC)2 is

Solution

Correct option is

6x + 12y = 297

.

Let the coordinate of R be (x, y), the

                    (PR)2 – (QR)2 = (AC)2

⇒ (x – 2)+ (y – 5)– [(x – 5)2 + (y – 11)2]= (7 – 1)2 + (15 –3)2

⇒ 6x + 12y + 4 – 121 = 36 + 144

⇒ 6x + 12y = 297    which is the locus of R.

SIMILAR QUESTIONS

Q1

ABCD is a rectangle with A(–1,2),B(3,7) and AB : BC = 4:3. If isthe center of the rectangle then the distance of p from each corner is equal to

Q2

If a (2,0) and (0,2) are given points and p is a point such that PA:PB = 2:3 then the locus of p passes through the point (a,a) for

Q3

If A(1, a), B(a, a2), C(a2, a2) are the vertices of a triangle which are equidistance from the origin, then the centroid of the triangle ABC is at the point

Q4

Given the point A(0, 4) and B(0, –4), the equation of the locus of the pointp(x, y) such that |AP – BP| = 6 is

Q5

Coordinate (x, y) of a point P satisfy the relation 3x + 4= 9, y = mx + 1. The number of integral value of m for which the x-coordinate of p is also an integer is

Q6

The point A(2, 3), B(3, 5), C(7, 7) and D(4, 5) are such that 

Q7

Q, R and are the points on the line joining the points P(a, x) and T(b, y) such that PQ = QR = RS = ST.

Q8

The line joining A(bcos α, bsin α) and B(acos β, asin β) is produced to point M(x, y) so that AM : MB = b : a, then 

Q9

OPQR is square and M, N are the middle points of the sides PQ and QRrespectively then the ratio of the areas of the square and the triangle OMNis

Q10

If px1x2….xi,….and q y1y2,…y… are in A.P. with common difference a and b respectively, then locus of the center of mean position of the point Ai (xi, yi), = 1, 2 …n is