Question

y = 2 x + 4.
20. Find the equations of the tangents to the circle x2 + y2 - 2x - 4y = 4 which are
perpendicular to the line 3x - 4y - 1 = 0.
+
which make an angle of 60° with​

Answer 1

Answer:

answr

search

What would you like to ask?

MATHS

Find the equation of the tangents to the circle x

2

+y

2

−2x−4y−20=0 which pass through the point (8,1).

Share

Study later

ANSWER

Any line through the point (8,1) is

y−1=m(x−8)

or mx−y+(1−8m)=0.....(1)

If it is a tangent then perpendicular from centre (1,2) is equal to radius

1+4+20

=5

∴

(m

2

+1)

m−2+(1−8m)

=5

or (−7m−1)

2

=25(m

2

+1)

or 49m

2

+14m+1=25m

2

+25

or 24m

2

+14m−24=0

or 12m

2

+7m−12=0

or 12m

2

+16m−9m−12=0

(3m+4)(4m−3)=0

∴m=−4/3,3/4.

Putting the values of m in (1), the required tangents are

4x+3y−35=0

and 3x−4y−20=0.