Question

Find the coordinates of centre of circle 2x2 + 2y2 - 3x + 5y - 7 =0​

Answer 1

$\huge{\underline{\sf{\red{Answer}}}}$

Given:

2x²+2y²-3x+5y-7=0 is the equation of the circle

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To find

★ Radius of the circle

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$\huge{\underline{\underline{\green{\tt{Formula}}}}}$

★c= (-g,-f)

★ General Equation of circle = x²+y²+2gx+2fy+c

★ g= $\dfrac{coefficient\:of\:x}{2}$

★ f= $\dfrac{coefficient\:of\:y}{2}$

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$\huge{\underline{\tt{SoluTion}}}$

Since the coefficient of x² and y² is not 1

therefore we need to divide whole equation by 2 so that it becomes the equation of circle

$\dfrac{\cancel{2}x^2}{\cancel{2}} + \dfrac{\cancel{2}y^2}{\cancel{2}} - \dfrac{3x}{2} +\dfrac{5y}{2} - \dfrac{7}{2} \\ \\ \implies x^2 +y^2 -\dfrac{3x}{2} + \dfrac{5y}{2} - \dfrac{7}{2}$

Here now

By applying Formulas

$g= \dfrac{-3}{2} \\ f= \dfrac{5}{2} \\ \\ \implies\large{\boxed{ c \bigg[ \bigg(\dfrac{3}{2}\bigg) , \bigg(\dfrac{-5}{2} \bigg) \bigg]}}$

Answer 2

Answer:

Given:

2x²+2y²-3x+5y-7=0 is the equation of the circle

__________________________________________________

To find

★ Radius of the circle

__________________________________________________

\huge{\underline{\underline{\green{\tt{Formula}}}}}

Formula

★c= (-g,-f)

★ General Equation of circle = x²+y²+2gx+2fy+c

★ g= \dfrac{coefficient\:of\:x}{2}

2

coefficientofx

★ f= \dfrac{coefficient\:of\:y}{2}

2

coefficientofy

__________________________________________________

\huge{\underline{\tt{SoluTion}}}

SoluTion

Since the coefficient of x² and y² is not 1

therefore we need to divide whole equation by 2 so that it becomes the equation of circle

\begin{lgathered}\dfrac{\cancel{2}x^2}{\cancel{2}} + \dfrac{\cancel{2}y^2}{\cancel{2}} - \dfrac{3x}{2} +\dfrac{5y}{2} - \dfrac{7}{2} \\ \\ \implies x^2 +y^2 -\dfrac{3x}{2} + \dfrac{5y}{2} - \dfrac{7}{2}\end{lgathered}

2

2

x

2

+

2

2

y

2

−

2

3x

+

2

5y

−

2

7

⟹x

2

+y

2

−

2

3x

+

2

5y

−

2

7

Here now

By applying Formulas

\begin{lgathered}g= \dfrac{-3}{2} \\ f= \dfrac{5}{2} \\ \\ \implies\large{\boxed{ c \bigg[ \bigg(\dfrac{3}{2}\bigg) , \bigg(\dfrac{-5}{2} \bigg) \bigg]}}\end{lgathered}

g=

2

−3

f=

2

5

⟹

c[(

2

3

),(

2

−5

)]