In a rectangle A B C D, the coordinates of A | vedclass

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

Question

$(a)$

Given,

$A B C D$ is a rectangle $A(1,2)$ and $B(3,6)$ equation of one of the diameter of circle circumscribing the rectangle is

$2 x-y+

Vedclass · Accepted Answer

$16$

Vedclass · Answer

$(a)$

Given,

$A B C D$ is a rectangle $A(1,2)$ and $B(3,6)$ equation of one of the diameter of circle circumscribing the rectangle is

$2 x-y+4=0 	ext {. }$

Slope of diameter $=2$

and slope of line $A B=\frac{6-2}{3-1}=\frac{4}{2}=2$

$	herefore$ Side $A B$ is parallel to diameter of circle equation of line $A B$

$y-2=2(x-1) \Rightarrow 2 x-y=0$

Distance between diameter of circle and line $A B$

$d=\left|\frac{4}{\sqrt{2^2+1}}ight|=\frac{4}{\sqrt{5}}$

$	herefore \quad B C=2 d=\frac{8}{\sqrt{5}}$

Now, $\quad A B=\sqrt{(3-1)^2+(6-2)^2}$

$=\sqrt{4+16}=2 \sqrt{\overline{5}}$

Area of rectangle $=A B 	imes B C$

$=2 \sqrt{5} 	imes \frac{8}{\sqrt{5}}=16$

In a rectangle $A B C D$, the coordinates of $A$ and $B$ are $(1,2)$ and $(3,6)$ respectively and some diameter of the circumscribing circle of $A B C D$ has equation $2 x-y+4=0$. Then, the area of the rectangle is

Similar Questions

Find the area of the triangle formed by the line $y-x=0, x+y=0$ and $x-k=0$.

A point moves such that its distance from the point $(4,\,0)$is half that of its distance from the line $x = 16$. The locus of this point is

The number of integral points (integral point means both the coordinates should be integer) exactly in the interior of the triangle with vertices $(0, 0), (0, 21)$ and $(21, 0)$, is

The point moves such that the area of the triangle formed by it with the points $(1, 5)$ and $(3, -7)$ is $21$ sq. unit. The locus of the point is