Suppose a, b are real numbers such that `ab ne 0`. Which of the following four figures represents the curve `(y -ax - b)(bx^(2) + ay^(2) - ab) = 0` ?

Options

A.
B.
C.
D.

Answer

B

Explanation

`y = ax + b` and ` (x^(2))/(a) + (y^(2))/(b) = 1`
slope `=a`
for the line, y intercept `= b`
Fig 1. for line `rarr a lt 0, b gt 0` hence the other fig. Cannot be an ellipse
Fig.2 `a gt 0, b lt 0` hence the fig. is a hyperbola
Similarly you can check rest 2 options