The combined equation of straight lines passing through point  $\left(-1,2\right)$ and each line makes intercepts on the coordinate axes whose product is   

detailed solution

Correct option is A

The equation of any line which makes x- intercept a and y- intercept b is  xa+yb=1Since the product of intercepts is equal to 1, one is the reciprocal of the other. It means a,1a  are intercepts of the line. Hence, the equation of the line can be written asxa+ay=1                                            ......(1) It is passing through the point  (-1,2)   −1a+2a=12a2−a−1=0 The roots of the equation are a=1,a=−12 Substitute a=1 in equation (1) It gives x+y−1=0 Substitute a=−12in equation (1) It gives −2x−12y=1−4x−y=24x+y+2=0 The combined equation of two lines is the product of both equationsTherefore, the combined equation of pair of lines is x+y−14x+y+2=0