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Question
The equation of circle passing through the origin and point of intersection of circle x2+y2−2x+4y−20=0 and line x+y−1=0 is
The equation of circle passing through the origin and point of intersection of circle x2+y2−2x+4y−20=0 and line x+y−1=0 is
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Solution
The correct option is A x2+y2−22x−16y=0
As the equation of circle passes through point of intersection of circles x2+y2−2x+4y−20=0 and line x+y−1=0Let the equation of required circle is (x2+y2−2x+4y−20)+λ(x+y−1)=0
Since, it passes through origin.
Therefore, −20−λ=0⇒λ=−20
Hence, the required equation of circle is
x2+y2−22x−16y=0.
As the equation of circle passes through point of intersection of circles x2+y2−2x+4y−20=0 and line x+y−1=0
Let the equation of required circle is (x2+y2−2x+4y−20)+λ(x+y−1)=0
Since, it passes through origin.
Therefore, −20−λ=0⇒λ=−20
Hence, the required equation of circle is
x2+y2−22x−16y=0.
Since, it passes through origin.
Therefore, −20−λ=0⇒λ=−20
Hence, the required equation of circle is
x2+y2−22x−16y=0.
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