AP EAMCET202120 Aug 2021Evening ShiftMathematicsCircleActual
The equation of the pair of straight lines parallel to x - axis and touching the circle x 2 + y 2 - 6 x - 4 y - 12 = 0 is
Options
- Ay 2 - 4 y - 21 = 0
- By 2 + 4 y - 21 = 0
- Cy 2 - 4 y + 21 = 0
- Dy 2 + 4 y + 21 = 0
Correct answer
A. y 2 - 4 y - 21 = 0
Step-by-step solution
Given that: x 2 + y 2 - 6 x - 4 y - 12 = 0 Centre of the circle: - g , - f = 3 , 2 Radius of the circle: r = g 2 + f 2 - c = 9 + 4 + 12 = 5 As we know that diameter is always perpendicular to the tangent. Hence, at the ends of the diameter perpendicular to x - axis , tangents will be parallel to x - axis . So, tangents at P 3 , 7   and Q = 3 , - 3 will be parallel to x - axis . Equation of line at P 3 , 7   and parallel to x - axis : y = 7   ⇒   y - 7 = 0 Equation of line at Q 3 , - 3