The diameters of a circle are along 2x + y - | vedclass

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

Question

(C) The intersection point of the diameter lines is the center of the circle. Solving the equations $2x + y = 7$ and $x + 3y = 11$:From the first equa

Vedclass · Accepted Answer

$x^2 + y^2 - 4x - 6y - 12 = 0$

Vedclass · Answer

(C) The intersection point of the diameter lines is the center of the circle. Solving the equations $2x + y = 7$ and $x + 3y = 11$:From the first equation,$y = 7 - 2x$.Substituting into the second: $x + 3(7 - 2x) = 11$ $\Rightarrow x + 21 - 6x = 11$ $\Rightarrow -5x = -10$ $\Rightarrow x = 2$.Then $y = 7 - 2(2) = 3$. So,the center $(h, k) = (2, 3)$.The circle passes through $(5, 7)$,so the radius $r$ is the distance between $(2, 3)$ and $(5, 7)$:$r = \sqrt{(5 - 2)^2 + (7 - 3)^2} = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = 5$.The equation of the circle is $(x - h)^2 + (y - k)^2 = r^2$:$(x - 2)^2 + (y - 3)^2 = 5^2$$x^2 - 4x + 4 + y^2 - 6y + 9 = 25$$x^2 + y^2 - 4x - 6y + 13 - 25 = 0$$x^2 + y^2 - 4x - 6y - 12 = 0$.

The diameters of a circle are along $2x + y - 7 = 0$ and $x + 3y - 11 = 0$. Then,the equation of this circle,which also passes through $(5, 7)$,is

Similar Questions

If the lines $2x - 3y = 5$ and $3x - 4y = 7$ are two diameters of a circle of radius $7$,then the equation of the circle is

Find the equation of a circle whose diameters are $2x - 3y = 5$ and $3x - 4y = 7$ and whose radius is $8$.

The sides of a rectangle are given by the equations $x=-2, x=4, y=-2$ and $y=5$. Then the equation of the circle,whose centre is the point of intersection of the diagonals,lying within the rectangle and touching only two opposite sides,is

The equation of the circle concentric with the circle $x^2 + y^2 - 4x - 6y - 3 = 0$ and touching the $y$-axis is:

$A$ circle passes through $(-2, 4)$ and touches the $y-$axis at $(0, 2).$ Which one of the following equations can represent a diameter of this circle?

Vedclass Test Series

Exam Paper Generator

Online Exam Module