Question

The equation of the pair of straight lines parallel to y-axis and which are tangents to the circle x²+y²-6x-4y-12=0

Answer 1

Answer:

The equation of the line parallel to x-axis is y = a.

=> y -a = 0 ..(i)

Equation of given circle is x2 + y2 – 6x – 4y – 12 = 0 …(ii)

Comparing (ii) with ax2 + by2 + 2gx + 2fy + c = 0

We get a = 1, b = 1, g = -3, f = -2, c = -12

Centre is (-g/a, -f/a) = (3, 2)

Radius = (1/a)√(g2 + f2 – ac)

= √(9 + 4 +12)

= 5

The perpendicular distance from the line to the centre is the radius.

So the distance from line y – a = 0 to the point (3, 2) is |2 – a| = 5

=> (2 – a) = ±5

=> 2 – a = 5 or 2 – a = -5

=> a = -3 or a = 7

So the equation or pair of straight lines is (y + 3)(y – 7) = 0

=> y2 – 4y – 21 = 0