CircleMedium
Question
Pair of tangents are drawn from every point on the line 3x + 4y = 12 on the circle x2 + y2 = 4. Their variable chord of contact always passes through a fixed point whose co-ordinates are -
Options
A.
B.
C.(1, 1)
D.
Solution
Let P(x1, y1) be a point on the line 3x + 4y = 12.
Equation of variable chord of contact of P(x1, y1) wrt circle x2 + y2 = 4
xx1 + yy1 - 4 = 0 ......(1)
Also 3x1 + 4y1 - 12 = 0
x1 +
y1 - 4 = 0 .....(2)Comparing (1) & (2)
x = 1, y =
∴ variable chord of contact always passes through (1,
)Create a free account to view solution
View Solution FreeMore Circle Questions
The locus of the mid-point of the chord of contact of tangents drawn from points lying on the straight line4x - 5y = 20 ...If P is a point of the ellipse = 1, whose foci are S and S′. Let ⎳PSS′ = α and ⎳PS′ S...If the centre, vertex and focus of a hyperbola be (0, 0), (4, 0) and (6, 0) respectively, then the equation of the hyper...The angle of intersection of circles x2 + y2 + 8x − 2y − 9 = 0 and x2 + y2 − 2x + 8y − 7 = 0 is ...The angle between the tangents drawn from the origin to the circle (x − 7)2 + (y + 1)2 = 25 is-...