The number of points on x -axis which are at a distance c(c

Question

The number of points on x -axis which are at a distance c(c<3) from the point (2,3) is (A) 2 (B) 1 (C) infinite (D) no point

Tardigrade Admin · Accepted Answer

Let a point on x -axis be (x1, 0), then its distance from the point (2,3)=√(x1-2)2+9=c or (x1-2)2=c2-9 ∴ x1-2=√c2-9 . But c< 3 ⇒ c2-9< 0 ∴ x1 will be imaginary.

Q. The number of points on $x$ -axis which are at a distance $c (c < 3)$ from the point $(2, 3)$ is

2

1

infinite

no point

Let a point on $x$ -axis be $(x_{1}, 0)$ , then its distance from the point $(2, 3) = (x_{1} - 2)^{2} + 9 = c$
or $(x_{1} - 2)^{2} = c^{2} - 9$
$∴ x_{1} - 2 = c^{2} - 9 .$
But $c < 3 \Rightarrow c^{2} - 9 < 0$
$∴ x_{1}$ will be imaginary.

Q. The number of points on x -axis which are at a distance c(c<3) from the point (2,3) is

2

1

infinite

no point

Let a point on x -axis be (x1​,0), then its distance from the point (2,3)=(x1​−2)2+9​=c or (x1​−2)2=c2−9 ∴x1​−2=c2−9​. But c<3⇒c2−9<0 ∴x1​ will be imaginary.

Q. The number of points on $x$ -axis which are at a distance $c (c < 3)$ from the point $(2, 3)$ is

Let a point on $x$ -axis be $(x_{1}, 0)$ , then its distance from the point $(2, 3) = (x_{1} - 2)^{2} + 9 = c$
or $(x_{1} - 2)^{2} = c^{2} - 9$
$∴ x_{1} - 2 = c^{2} - 9 .$
But $c < 3 \Rightarrow c^{2} - 9 < 0$
$∴ x_{1}$ will be imaginary.