# The Sides of a Square Are X = 6, X = 9, Y = 3 and Y = 6. Find the Equation of a Circle Drawn on the Diagonal of the Square as Its Diameter. - Mathematics

The sides of a square are x = 6, x = 9, y = 3 and y = 6. Find the equation of a circle drawn on the diagonal of the square as its diameter.

#### Solution

According to the question:
Sides of the square are x = 6, x = 9, y = 3 and y = 6.
The vertices of the square are (6, 6), (9, 6), (9, 3) and (6, 3).
And, the vertices of two diagonals are (6, 6), (9, 3) and (9, 6), (6, 3).
Hence, the equation of the circle is $\left( x - 6 \right)\left( x - 9 \right) + \left( y - 6 \right)\left( y - 3 \right)$ or

$x^2 + y^2 - 15x - 9y + 72 = 0$
Concept: Circle - Standard Equation of a Circle
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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 24 The circle
Exercise 24.3 | Q 3 | Page 37