If a point P moves such that the sum of the d | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Let the point be $P(x, y)$. The given condition is $PA + PB = 4$.$\sqrt{(x-1)^2 + (y+1)^2} + \sqrt{(x+1)^2 + (y-1)^2} = 4$Squaring both sides:$(x-

Vedclass · Accepted Answer

$3x^2 + 2xy + 3y^2 = 8$

Vedclass · Answer

(B) Let the point be $P(x, y)$. The given condition is $PA + PB = 4$.$\sqrt{(x-1)^2 + (y+1)^2} + \sqrt{(x+1)^2 + (y-1)^2} = 4$Squaring both sides:$(x-1)^2 + (y+1)^2 + (x+1)^2 + (y-1)^2 + 2\sqrt{((x-1)^2 + (y+1)^2)((x+1)^2 + (y-1)^2)} = 16$$2(x^2 + y^2 + 2) + 2\sqrt{(x^2 + y^2 + 2 - 2x + 2y)(x^2 + y^2 + 2 + 2x - 2y)} = 16$$(x^2 + y^2 + 2) + \sqrt{(x^2 + y^2 + 2)^2 - (2x - 2y)^2} = 8$$\sqrt{(x^2 + y^2 + 2)^2 - 4(x - y)^2} = 8 - (x^2 + y^2 + 2)$Squaring again:$(x^2 + y^2 + 2)^2 - 4(x - y)^2 = (6 - (x^2 + y^2))^2$$(x^2 + y^2 + 2)^2 - (x^2 + y^2 - 6)^2 = 4(x - y)^2$Using $a^2 - b^2 = (a-b)(a+b)$:$((x^2 + y^2 + 2) - (x^2 + y^2 - 6))((x^2 + y^2 + 2) + (x^2 + y^2 - 6)) = 4(x^2 + y^2 - 2xy)$$(8)(2x^2 + 2y^2 - 4) = 4(x^2 + y^2 - 2xy)$$16(x^2 + y^2 - 2) = 4(x^2 + y^2 - 2xy)$$4x^2 + 4y^2 - 8 = x^2 + y^2 - 2xy$$3x^2 + 2xy + 3y^2 = 8$

If a point $P$ moves such that the sum of the distances from $P$ to the points $A(1, -1)$ and $B(-1, 1)$ is always $4$,then the equation for the locus of $P$ is

Similar Questions

The image of every point lying on the curve $x^2+y^2=1$ in the line $x+y=1$ satisfies the equation:

$A$ variable circle passes through a fixed point $A(p, q)$ and touches the $x$-axis. The locus of the other end of the diameter passing through $A$ is:

The locus of a point,such that the difference of the squares of the lengths of the tangents drawn from it to two given circles is constant,is:

The equation of the locus of the midpoints of the chords of the circle $4x^2 + 4y^2 - 12x + 4y + 1 = 0$ that subtend an angle of $\frac{2\pi}{3}$ at its center is

The locus of the centre of the circle,which cuts the circle $x^2+y^2-20x+4=0$ orthogonally and touches the line $x=2$,is

Vedclass Test Series

Exam Paper Generator

Online Exam Module