Question

Question 3 Find the equation of the circle with centre (1/2, 1/4) and radius 1/12

Class X1 - Maths -Conic Sections Page 241

Answer 1

concept : if (h,k) is the centre of cirlce and r is the radius of that circle then, equation of cirlce is (x - h)² + (y -k)² = r²

here,
Centre of circle = ( 1/2 , 1/4)
radius of cirlce = 1/12

equation of circle is
(x - 1/2)² + (y - 1/4)² = (1/12)²
x² + 1/4 - x + y² + 1/16 - y/2 = 1/144
x² + y² - x -y/2 + 1/4 + 1/16 - 1/144 = 0
x² + y² - x - y/2 + (36 + 9 -1)/144 = 0
x² + y² - x - y/2 + (44)/144 = 0
x² + y² - x -y/2 + 11/36 = 0
36x² + 36y² -36x - 18y + 11= 0

hence, equation of cirlce is , 36x² + 36y² -36x - 18y + 11 = 0

Answer 2

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Question 3 Find the equation of the circle with centre (1/2, 1/4) and radius 1/12

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The equation of a circle with centre (h, k) -

And radius r is given = (1/12)

It is given that centre (h, k) = (1/2 , 1,4)

radius (r) = (1/12)

Therefore the equation of circle is -

(x+h)²+(y+k)²= (r)²

(x+ 1/2)²+(y + 1/4)²= (1/12)²

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36x²+36y²-36x-18y+11 = 0

Hence equn of circle = 36x²+36y²-36x-18y+11=0

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