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

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 x² + y² + 2x + 4y – p = 0 and the coordinate axes have exactly three common points?

Share with your friends

Talk Doctor Online in Bissoy App

Salim Ahmed Kawsar · Answer 1 · Feb 05, 2023 15:29:48

Centre (–1, –2)
Geometrically, circle will have exactly 3 common points with axes in the cases
(i) Passing through origin => p = 0
(ii) Touching x-axis and intersecting y-axis at two
points i.e. f² > C and g² = C.
i.e. 4 > – p and 1 = –p
=> p > –4 and p = –1
=> p = –1
(iii) Touching y-axis and intersecting x-axis at two points i.e. f² = c and g² > C
=> 4 = –p and 1 > –p
=> p = –4 and p > –1
which is not possible.
∴ Only two values of p are possible.

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,

1 Answers