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Standard IX

Mathematics

Every Point on the Bisector of an Angle Is Equidistant from the Sides of the Angle.

Find the equa...

Question

Find the equation of the circle drawn on a diagonal of the rectangle as it diameter whose sides are $x + 1 = 0, y + 1 = 0, x - 4 = 0 a n d y - 2 = 0.$

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Solution

Sides of the rectangle $:$
$x + 1 = 0, x - 4 = 0$
$y + 1 = 0, y - 2 = 0$
Vertices are $:$ $A (1, - 1)$ $B (1, 2)$ $D (4, - 1)$ $C (4, 2)$
diagonal $A C :$ $(y + 1) / (x - 1)$ $=$ $(2 - (- 1)) / (4 - 1) = 1$
$y = x - 2$
diagonal $B D :$ $(y - 2) / (x - 1)$ $=$ $(- 1 - 2) / (4 - 1)$
$y = - x + 3$

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Find the equation of the circle drawn on a diagonal of the rectangle as it diameter whose sides are x+1=0,y+1=0,x−4=0andy−2=0.

Sides of the rectangle:x+1=0,x−4=0y+1=0,y−2=0Vertices are: A(1,−1) B(1,2) D(4,−1) C(4,2)diagonal AC: (y+1)/(x−1) = (2−(−1))/(4−1)=1y=x−2diagonal BD: (y−2)/(x−1) = (−1−2)/(4−1)y=−x+3

Find the equation of the circle drawn on a diagonal of the rectangle as it diameter whose sides are $x + 1 = 0, y + 1 = 0, x - 4 = 0 a n d y - 2 = 0.$

Sides of the rectangle $:$
$x + 1 = 0, x - 4 = 0$
$y + 1 = 0, y - 2 = 0$
Vertices are $:$ $A (1, - 1)$ $B (1, 2)$ $D (4, - 1)$ $C (4, 2)$
diagonal $A C :$ $(y + 1) / (x - 1)$ $=$ $(2 - (- 1)) / (4 - 1) = 1$
$y = x - 2$
diagonal $B D :$ $(y - 2) / (x - 1)$ $=$ $(- 1 - 2) / (4 - 1)$
$y = - x + 3$