For any real number lambda neq 1,the centre o | vedclass

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

Question

(A) Let the circle pass through $A(1, \lambda)$,$B(\lambda, 1)$,and $C(\lambda, \lambda)$.Since the points $B(\lambda, 1)$ and $C(\lambda, \lambda)$ h

Vedclass · Accepted Answer

$\left(\frac{1+\lambda}{2}, \frac{1+\lambda}{2}\right)$

Vedclass · Answer

(A) Let the circle pass through $A(1, \lambda)$,$B(\lambda, 1)$,and $C(\lambda, \lambda)$.Since the points $B(\lambda, 1)$ and $C(\lambda, \lambda)$ have the same $x$-coordinate,the perpendicular bisector of $BC$ is the horizontal line $y = \frac{1+\lambda}{2}$.Since the points $A(1, \lambda)$ and $C(\lambda, \lambda)$ have the same $y$-coordinate,the perpendicular bisector of $AC$ is the vertical line $x = \frac{1+\lambda}{2}$.The centre of the circle is the intersection of these perpendicular bisectors.Therefore,the centre is $\left(\frac{1+\lambda}{2}, \frac{1+\lambda}{2}\right)$.

For any real number $\lambda \neq 1$,the centre of the circle that passes through $A(1, \lambda)$,$B(\lambda, 1)$,and $C(\lambda, \lambda)$ is

Similar Questions

The number of tangents that can be drawn from $(0, 0)$ to the circle $x^2 + y^2 + 2x + 6y - 15 = 0$ is

The circumference of a circle passing through the point $(4,6)$ with two normals represented by $2x - 3y + 4 = 0$ and $x + y - 3 = 0$ is (in $\pi$)

If in two circles,arcs of the same length subtend angles $30^{\circ}$ and $78^{\circ}$ at the centre,then the ratio of their radii is

The number of common tangents to the circles $x^2+y^2-x=0$ and $x^2+y^2+x=0$ is/are:

If the straight line $y = mx$ is outside the circle $x^2 + y^2 - 20y + 90 = 0$,then

Vedclass Test Series

Exam Paper Generator

Online Exam Module