First slide

Definition of a circle

Question

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?

Moderate

A

3x-4y-24=0
B

3x+4y-6=0
C

4x+3y-8=0
D

4x-3y+17=0

Solution

Using family of circles, the required circle will be of the form ${(x - 0)}^{2} + {(y - 4)}^{2} + λ x = 0$
$\begin{array}{l} Given, it passes through (2, 0) \Rightarrow 4 + 16 + 2 λ = 0 \Rightarrow λ = - 10 \\ So, the circle will be x^{2} + y^{2} - 10 x - 8 y + 16 = 0 having center at (5, 4) and radius as \end{array}$
$\sqrt{5^{2} + 4^{2} - 16} = 5$
For a line to be tangent, perpendicular distance from center should be equal to radius.
So, check the options and we get 4x+3y-8=0 is not tangent

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