Let P≡a,0, Q≡-1,0 and R≡2,0 are three given points. If the locus of the point S satisfying the relation SQ^2+SR^2=2SP^2 is 2x+3=0, then the sum of all…

Question

Let P≡a,0, Q≡-1,0 and R≡2,0 are three given points. If the locus of the point S satisfying the relation SQ^2+SR^2=2SP^2 is 2x+3=0, then the sum of all possible values of a is

MARKS Content Team · Accepted Answer

Correct answer: (D) -3. We have, P≡a,0,Q≡-1,0,R≡2,0 . Let, S≡x,y Now, given that SQ^2+SR^2=2SP^2. Hence, x+1^2+y^2+x-2^2+y^2=2x-a^2+y^2 or 2x^2+2y^2-2x+5=2x^2+2y^2-4ax+2a^2 or 4a-2x=2a^2-5 or 2x+3=0 or x=(-3)/2=(2a^2-5)/(4a-2) ⇒a=1,-4

Let $P \equiv (a, 0), Q \equiv (- 1, 0)$ and $R \equiv (2, 0)$ are three given points. If the locus of the point $S$ satisfying the relation $S Q^{2} + S R^{2} = 2 S P^{2}$ is $2 x + 3 = 0$ , then the sum of all possible values of $a$ is

Solution

More Straight Lines Questions

Let P≡a,0, Q≡-1,0 and R≡2,0 are three given points. If the locus of the point S satisfying the relation SQ2+SR2=2SP2 is 2x+3=0, then the sum of all possible values of a is

Solution

More Straight Lines Questions

Let $P \equiv (a, 0), Q \equiv (- 1, 0)$ and $R \equiv (2, 0)$ are three given points. If the locus of the point $S$ satisfying the relation $S Q^{2} + S R^{2} = 2 S P^{2}$ is $2 x + 3 = 0$ , then the sum of all possible values of $a$ is