The equation of the circle touching the lines | vedclass

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

Question

(A) The given equation $|x-2|+|y-3|=4$ represents a square with vertices at $(2+4, 3) = (6, 3)$,$(2-4, 3) = (-2, 3)$,$(2, 3+4) = (2, 7)$,and $(2, 3-4)

Vedclass · Accepted Answer

$x^2+y^2-4x-6y+5=0$

Vedclass · Answer

(A) The given equation $|x-2|+|y-3|=4$ represents a square with vertices at $(2+4, 3) = (6, 3)$,$(2-4, 3) = (-2, 3)$,$(2, 3+4) = (2, 7)$,and $(2, 3-4) = (2, -1)$.This square is centered at $(2, 3)$ and has a side length of $4\sqrt{2}$.The circle touching these lines is the incircle of this square.The center of the circle is the same as the center of the square,which is $(h, k) = (2, 3)$.The radius $r$ of the incircle is half the distance between parallel sides,or the perpendicular distance from the center $(2, 3)$ to any of the lines,such as $(x-2)+(y-3)=4 \implies x+y-9=0$.The distance $r = \frac{|2+3-9|}{\sqrt{1^2+1^2}} = \frac{|-4|}{\sqrt{2}} = 2\sqrt{2}$.The equation of the circle is $(x-h)^2+(y-k)^2=r^2$.Substituting the values: $(x-2)^2+(y-3)^2=(2\sqrt{2})^2$.$x^2-4x+4+y^2-6y+9=8$.$x^2+y^2-4x-6y+5=0$.

The equation of the circle touching the lines $|x-2|+|y-3|=4$ is

Similar Questions

The equation of the circle having its centre on the line $2x + y + 3 = 0$ and having the lines $3x + 4y - 18 = 0$ and $3x + 4y + 2 = 0$ as tangents is:

The centres of the circles $x^2 + y^2 = 1$,$x^2 + y^2 + 6x - 2y = 1$ and $x^2 + y^2 - 12x + 4y = 1$ are

$A$ circle has its equation in the form $x^2 + y^2 + 2x + 4y + 1 = 0$. Choose the correct coordinates of its centre and the right value of its radius from the following:

The circle possessing $y$-axis as its tangent at $(0,2)$ and passing through $(-1,0)$,also passes through

The circle $x^2+y^2-8x-12y+\alpha=0$ lies in the first quadrant without touching the coordinate axes. If $(6, 6)$ is an interior point to the circle,then

Vedclass Test Series

Exam Paper Generator

Online Exam Module