JEE Main · 2020 · 09 Jan 2020 · Shift 1 · Circle

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?

(A) $3 x - 4 y - 24 = 0$
(B) $3 x + 4 y - 6 = 0$
(C) $4 x - 3 y + 17 = 0$
(D) $4 x + 3 y - 8 = 0$ ✓ Correct

Answer: (D)

Solution

Touching the

y

-axis at

(0, 4)

places the centre at

(h, 4)

with radius

h

. Passing through

(2, 0)

gives

(2 - h)^{2} + 16 = h^{2}

, that is

20 - 4 h = 0

, so

h = 5

; the circle is centred at

(5, 4)

with radius

5

. A line is tangent when its distance from the centre equals

5

. For

4 x + 3 y - 8 = 0

that distance is

\frac{∣20 + 12 - 8∣}{5} = \frac{24}{5}

, which is not

5

, so this line is not a tangent.

JEE Main · 2020 · 09 Jan 2020 · Shift 1 · Single correct option

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