The equation of the circle passing through (2 | vedclass

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

Question

(A) Let the points be $A(2,0)$ and $B(0,4)$. The circle with minimum radius passing through two points has the line segment joining these points as it

Vedclass · Accepted Answer

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

Vedclass · Answer

(A) Let the points be $A(2,0)$ and $B(0,4)$. The circle with minimum radius passing through two points has the line segment joining these points as its diameter. The diameter of the circle is the distance $AB = \sqrt{(0-2)^2 + (4-0)^2} = \sqrt{4 + 16} = \sqrt{20}$. The radius $r = \frac{\sqrt{20}}{2} = \sqrt{5}$. The center of the circle is the midpoint of $AB$,which is $(\frac{2+0}{2}, \frac{0+4}{2}) = (1, 2)$. The equation of the circle with center $(h, k)$ and radius $r$ is $(x-h)^2 + (y-k)^2 = r^2$. Substituting the values,we get $(x-1)^2 + (y-2)^2 = 5$. Expanding this,we get $x^2 - 2x + 1 + y^2 - 4y + 4 = 5$. Simplifying,$x^2 + y^2 - 2x - 4y = 0$.

The equation of the circle passing through $(2,0)$ and $(0,4)$ and having the minimum radius is:

Similar Questions

The equation of the chord of the circle $x^2 + y^2 = a^2$ having $(x_1, y_1)$ as its mid-point is

The equation of a circle passing through the point $(2,8)$,touching the lines $4x-3y-24=0$ and $4x+3y-42=0$,and having the $x$-coordinate of its centre less than or equal to $8$ is

Given three collinear points $A(3,1)$,$B(7,-1)$,and $C(5,0)$. The length of a tangent drawn from $A$ to any circle that passes through $B$ and $C$ is ....... units.

Let $PQ$ and $RS$ be tangents at the extremities of a diameter $PR$ of a circle of radius $r$ such that $PS$ and $RQ$ intersect at a point $X$ on the circumference of the circle,then $2r$ equals

If $P(0,0), Q(1,0)$ and $R\left(\frac{1}{2}, \frac{\sqrt{3}}{2}\right)$ are three given points, then the centre of the circle for which the lines $PQ, QR$ and $RP$ are the tangents is

Vedclass Test Series

Exam Paper Generator

Online Exam Module