CircleEasy
Question
If the line 3x - 4y - k = 0 (k > 0) touches the circle x2 + y2 - 4x - 8y - 5 = 0 at (a, b) then k + a + b is equal to :-
Options
A.20
B.22
C.-30
D.-28
Solution
Since, the given line touches the given circle, the length of the perpendicular from the centre (2, 4) of the circle to the line 3x - 4y - k = 0 is equal to the radius 
= 5 of the circle.
∴
= ± 5
⇒ k = 15 [∵ k > 0]
hence equation of tangent is 3x - 4y - 15 = 0 ..... (1)
Let equation of normal to circle 4x + 3y = λ
It passes through centre (2, 4)
⇒ λ = 20
hence equation of normal is
4x + 3y = 20 .... (2)
Solve (1) & (2)
a = 5, b = 0
k + a + b = 15 + 5 + 0 = 20
= 5 of the circle.∴
= ± 5⇒ k = 15 [∵ k > 0]
hence equation of tangent is 3x - 4y - 15 = 0 ..... (1)
Let equation of normal to circle 4x + 3y = λ
It passes through centre (2, 4)
⇒ λ = 20
hence equation of normal is
4x + 3y = 20 .... (2)
Solve (1) & (2)
a = 5, b = 0
k + a + b = 15 + 5 + 0 = 20
Create a free account to view solution
View Solution FreeMore Circle Questions
The locus of the center of a circle which touches externally the circle, x2 + y2 - 6x - 6y + 14 = 0 and also touches the...Equations of four circles are $(x \pm a)^{2} + (y \pm a)^{2} = a^{2}$, then:...The equation of the circum-circle of the triangle formed by the lines x = 0, y = 0, = 1, is -...If y = c is a tangent to the circle x2 + y2 - 2x + 2y -2 = 0, then the value of c can be -...The equations of tangents to the circle x2 + y2 − 22x − 4y + 25 = 0 which are perpendicular to the line 5x +...