Question

The point on x-axis which is at a distance 12 unit from the point (4, 6) is ___________

(a) (-4 + \( \sqrt {11i} \), 0), (-4 – \( \sqrt {11i} \), 0)

(b) (-4 – \( \sqrt {11i} \), 0), (4 – \( \sqrt {11i} \), 0)

(c) (4 – \( \sqrt {11i} \), 0), (4 – \( \sqrt {11i} \), 0)

(d) (4 + \( \sqrt {11i} \), 0), (4 – \( \sqrt {11i} \), 0)

The question was posed to me by my college professor while I was bunking the class.

The doubt is from Geometry in division Coordinate Geometry of Mathematics – Class 10

Answer 1

The correct answer is (d) (4 + \( \sqrt {11i} \), 0), (4 – \( \sqrt {11i} \), 0)

For explanation I would say: Let the point on x-axis be (x, 0)

Distance between (4, 6) and (x, 0) = \( \sqrt {(x_2-x_1)^2 + (y_2-y_1)^2} \)

= \( \sqrt {(x-4)^2 + (0-6)^2} \)

= \( \sqrt {x^2-8x + 16 + 36} \)

= \( \sqrt {x^2-8x + 52} \)

The distance between (4, 6) and (x, 0) is 12

∴ \( \sqrt {x^2-8x + 52} \) = 12

Squaring on both sides, we get,

x^2 – 8x + 52 = 25

x^2 – 8x + 27 = 0

x = 4 + \( \sqrt {11i} \), 4 – \( \sqrt {11i} \)