COMEDK2018MathematicsStraight Lines
The locus of the mid-point of the intercept of the line x +y =p between the coordinate axes is
Options
- Ax⁻²+y⁻²=4 p⁻²
- Bx⁻²+y⁻²=p⁻²
- Cx²+y²=4 p⁻²
- Dx²+y²=p²
Correct answer
A. x⁻²+y⁻²=4 p⁻²
Step-by-step solution
Given, line segment is x +y =p Therefore, it cuts the X -axis and Y -axis at points (p , 0) and (0, p cosec ) . Hence, the coordinate of the mid point are ( p 2 , p cosec 2 ) Therefore, x= p 2 and y= p cosec 2 or = p 2 x and = p 2 y ² + ² =1 ( p 2 x )²+ ( p 2 y )²=1 p² 4 x² + p² 4 y² =1 1 4 x² + 1 4 y² = 1 p² 1 x² + 1 y² = 4 p² x⁻²+y⁻²=4 p⁻²