Test Index

Circles Part 1

Section: Mathematics

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Question : 37 of 100

Marks: +1, -0

A circle touches the y-axis at the point (0, 4) and passes through the point (2, 0). Which of the following lines is not a tangent to this circle ?

[9 Jan 2020 Shift 1]

3x - 4y - 24 = 0
3x + 4y - 6 = 0
4x + 3y - 8 = 0
4x - 3y + 17 = 0

Solution:

Equation of family of circle touching y-axis at (0, 4) is given by

(x - 0)^2 + (y - 4)^2 + \lambda x = 0

.

It passes through (2, 0)

\Rightarrow \lambda = -10.

⇒ Required circle is

(x - 0)^2 + (y - 4)^2 - 10x = 0

\Rightarrow x^2 + y^2 - 10x - 8y + 16 = 0

center of circle = (5,4) and radius = 5

distance of 4x + 3y - 8 = 0 from (5, 4)

= \left| \frac{24}{5} \right| \neq \text{radius}

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