A circle S touches the Y-axis at (0,3) and ma | vedclass

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

Question

(C) The equation of a circle that touches the $Y$-axis at $(0,3)$ is given by $(x-a)^2 + (y-3)^2 = a^2$,which simplifies to $x^2 + y^2 - 2ax - 6y + 9

Vedclass · Accepted Answer

$5$

Vedclass · Answer

(C) The equation of a circle that touches the $Y$-axis at $(0,3)$ is given by $(x-a)^2 + (y-3)^2 = a^2$,which simplifies to $x^2 + y^2 - 2ax - 6y + 9 = 0$.Since the length of the intercept on the $X$-axis is $8$ units,we use the formula $2\sqrt{g^2 - c} = 8$,where $g = -a$ and $c = 9$.$2\sqrt{(-a)^2 - 9} = 8$ $\Rightarrow \sqrt{a^2 - 9} = 4$ $\Rightarrow a^2 - 9 = 16$ $\Rightarrow a^2 = 25$ $\Rightarrow a = \pm 5$.Since the centre $C(a, 3)$ lies in the second quadrant,$a$ must be negative,so $a = -5$.Thus,the centre is $C(-5, 3)$.The distance of $C(-5, 3)$ from the point $(-2, -1)$ is $\sqrt{(-2 - (-5))^2 + (-1 - 3)^2} = \sqrt{(3)^2 + (-4)^2} = \sqrt{9 + 16} = \sqrt{25} = 5$.

$A$ circle $S$ touches the $Y$-axis at $(0,3)$ and makes an intercept of length $8$ units on the $X$-axis. If the centre $C$ of the circle $S$ lies in the second quadrant,then the distance of $C$ from the point $(-2,-1)$ is

Similar Questions

If the line $x + 2by + 7 = 0$ is a diameter of the circle $x^2 + y^2 - 6x + 2y = 0$,then $b = $

The points $A, B, C, D, E$ are marked on the circumference of a circle in clockwise direction such that $\angle ABC = 130^{\circ}$ and $\angle CDE = 110^{\circ}$. The measure of $\angle ACE$ in degrees is: (in $^{\circ}$)

The area of the circle passing through the points $(5, 2), (5, -2),$ and $(1, 2)$ is (in $\pi$)

If the lines $3x - 4y + 4 = 0$ and $6x - 8y - 7 = 0$ are tangents to a circle,then the radius of the circle is

$A$ person $X$ is running around a circular track,completing one round every $40 \ s$. Another person $Y$ running in the opposite direction meets $X$ every $15 \ s$. The time,expressed in seconds,taken by $Y$ to complete one round is

Vedclass Test Series

Exam Paper Generator

Online Exam Module