A circle with center at (2,4) is such that th | vedclass

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

Question

(A) Let $r$ be the radius of the circle. The center of the circle is $C(2,4)$.The perpendicular distance $d$ from the center $(2,4)$ to the line $x+y+

Vedclass · Accepted Answer

$\sqrt{41}$

Vedclass · Answer

(A) Let $r$ be the radius of the circle. The center of the circle is $C(2,4)$.The perpendicular distance $d$ from the center $(2,4)$ to the line $x+y+2=0$ is given by:$d = \frac{|2+4+2|}{\sqrt{1^2+1^2}} = \frac{8}{\sqrt{2}} = 4\sqrt{2}$.The chord length is $6$,so the distance from the center to the chord bisects the chord into two segments of length $3$. Let $A$ be the foot of the perpendicular from $C$ to the chord and $B$ be a point on the circle where the chord meets it.In the right-angled triangle $	riangle CAB$,by the Pythagorean theorem:$r^2 = (AC)^2 + (AB)^2$$r^2 = (4\sqrt{2})^2 + (3)^2$$r^2 = 32 + 9 = 41$$r = \sqrt{41}$.

Types of Microbes	Scientific Name	Commercial Product
Bacterium	$A$	Clot buster enzyme
$B$	Aspergillus niger	Citric acid
Fungus	Trichoderma polysporum	$C$
Bacterium	$D$	Butyric acid

$A$ circle with center at $(2,4)$ is such that the line $x+y+2=0$ cuts a chord of length $6$. The radius of the circle is

Similar Questions

Let $n(U) = 700, n(A) = 200, n(B) = 300$ and $n(A \cap B) = 100,$ then $n(A^c \cap B^c) = $

Identify the blank spaces $A, B, C$ and $D$ given in the following table and select the correct answer.
Types of Microbes Scientific Name Commercial Product
Bacterium $A$ Clot buster enzyme
$B$ Aspergillus niger Citric acid
Fungus Trichoderma polysporum $C$
Bacterium $D$ Butyric acid

$\frac{(1+i)^{2011}}{(1-i)^{2009}}$ is equal to

Let $f(x) = \frac{2\sin^2 x - 1}{\cos x} + \frac{\cos x(2\sin x + 1)}{1 + \sin x}$. Then find $\int e^x (f(x) + f'(x)) dx$ (where $c$ is the constant of integration).

The volume-temperature graphs of a given mass of an ideal gas at constant pressures are shown below. What is the correct order of pressures?

Vedclass Test Series

Exam Paper Generator

Online Exam Module