The least distance of the point (10, 7) from | vedclass

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

Question

(D) The given equation of the circle is $x^2 + y^2 - 4x - 2y - 20 = 0$. Comparing this with the standard form $x^2 + y^2 + 2gx + 2fy + c = 0$,we get $

Vedclass · Accepted Answer

$5$

Vedclass · Answer

(D) The given equation of the circle is $x^2 + y^2 - 4x - 2y - 20 = 0$. Comparing this with the standard form $x^2 + y^2 + 2gx + 2fy + c = 0$,we get $g = -2$,$f = -1$,and $c = -20$. The center of the circle is $C = (-g, -f) = (2, 1)$. The radius $r$ is given by $\sqrt{g^2 + f^2 - c} = \sqrt{(-2)^2 + (-1)^2 - (-20)} = \sqrt{4 + 1 + 20} = \sqrt{25} = 5$. Let the point be $P = (10, 7)$. The distance $d$ between the point $P$ and the center $C$ is $\sqrt{(10 - 2)^2 + (7 - 1)^2} = \sqrt{8^2 + 6^2} = \sqrt{64 + 36} = \sqrt{100} = 10$. Since the distance $d = 10$ is greater than the radius $r = 5$,the point lies outside the circle. The least distance of the point from the circle is $d - r = 10 - 5 = 5$ units.

The least distance of the point $(10, 7)$ from the circle $x^2 + y^2 - 4x - 2y - 20 = 0$ is

Similar Questions

Let the centre of the circle $S=0$ lie on the line $x+y-5=0$ and also lie in the first quadrant. If this circle touches both the lines $x-2=0$ and $y-5=0$,then the area of the circle is

Find the equation of the diameter of the circle $x^2 + y^2 - 4x + 2y - 11 = 0$ which corresponds to the system of parallel chords $x - 2y + c = 0$.

If the shortest distance from $(2,-14)$ to the circle $x^2+y^2+6x+4y-12=0$ is $d$ and the length of the tangent drawn from the same point to the circle is $l$,then $\sqrt{d+l}=$

Given $r_1, r_2 > 0$ and $C_1, C_2$ are the centres of two circles having only two common tangents. If $C_1 C_2 = r_1 + r_2$,which of the following is correct?

If $A(-1,3)$ and $B(5,3)$ are points on a circle $C$ and the chord $AB$ subtends an angle $\pi / 4$ at a point $P$ on $C$,then the equation of such a circle $C$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module