For how many values of p, the circle x^2 + y^2 + 2x + 4y - p=0 and the coordinate axes have exactly three common points?

Question

Saurabh Koranglekar · Answer

Arun · Answer

x 2 + y 2 + 2 x + 4 y − p = 0 C a s e ( I ) ( 0 ) 2 + ( 0 ) 2 + 0 + 0 p = 0 C a s e ( I I ) g 2 − c = 0 f 2 − c > 0 1 − ( − p ) = 0 p = − 1 4 − ( − p ) > 0 p > − 4 C a s e ( I I I ) f 2 − c = 0 4 − ( p ) = 0 p = − 4 g 2 − c > 0 1 − ( − p ) > 0 p > − 1 ∴ Total 2 values of p, the circle and the co-ordinate have 3 common point.

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For how many values of p, the circle x^2 + y^2 + 2x + 4y - p=0 and the coordinate axes have exactly three common points?

For how many values of p, the circle x^2 + y^2 + 2x + 4y - p=0 and the coordinate axes have exactly three common points?

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