You visited us 5 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Perpendicular Distance of a Point from a Line

A point moves...

Question

A point moves such that its distance from the point (4, 0) is half that of its distance from the line x = 16. the locus of the point is
(a) 3x² + 4y² = 192
(b) 4x² + 3y² = 192
(c) x² + y² = 12
(d) none of these

Open in App

Solution

Let us suppose the point is P(x, y).
According to given condition
$\sqrt{{(x - 4)}^{2} + {(y - 0)}^{2}} = \frac{1}{2} |\frac{x - 16}{\sqrt{1^{2} + 0^{2}}}| i . e . \sqrt{{(x - 4)}^{2} + y^{2}} = \frac{1}{2} |x - 16| i . e . 4 [{(x - 4)}^{2} + y^{2}] = {(x - 16)}^{2} i . e . 4 [{(x - 4)}^{2} + y^{2}] = {(x - 16)}^{2} i . e . 4 [x^{2} + 16 - 8 x + y^{2}] = x^{2} + {(16)}^{2} - 32 x i . e . 4 x^{2} + 64 - 32 x + 4 y^{2} = x^{2} + {(16)}^{2} - 32 x i . e . 3 x^{2} + 4 y^{2} = 192$

Hence, the correct answer is option A.

Suggest Corrections

Similar questions

Q. A point moves such that its distance from the point

(4, 0)

is half that of its distance from the line

x = 16

, find its locus.

A point P moves so that its distance from the point (a, 0) is always equal to its distance from the line x + a = 0. The

locus of the point is

Q. A point moves so that its distance from the point

(2, 0)

is always

\frac{1}{3}

of its distance from the line

x - 18 = 0.

If the locus of the point is a conic, then

A point moves in such a way that the sum of square of its distance from the points A(2, 0) and B(-2, 0) is always

equal to the square of the distance between A and B. The locus of the point is

Q. A point moves so that its distance from y-axis is half of its distance from the origin. Find the locus of the point.

Join BYJU'S Learning Program

A point moves such that its distance from the point (4, 0) is half that of its distance from the line x = 16. the locus of the point is
(a) 3x² + 4y² = 192
(b) 4x² + 3y² = 192
(c) x² + y² = 12
(d) none of these

COURSES

EXAMS

CLASSES

EXAM PREPARATION

RESOURCES

COMPANY

FOLLOW US

FREE TEXTBOOK SOLUTIONS

STATE BOARDS

FOLLOW US

A point moves such that its distance from the point (4, 0) is half that of its distance from the line x = 16. the locus of the point is (a) 3x2 + 4y2 = 192 (b) 4x2 + 3y2 = 192 (c) x2 + y2 = 12 (d) none of these

Let us suppose the point is P(x, y). According to given condition x-42+y-02=12x-1612+02i.e.x-42+y2=12x-16i.e.4x-42+y2=x-162i.e.4x-42+y2=x-162i.e.4x2+16-8x+y2=x2+162-32xi.e.4x2+64-32x+4y2=x2+162-32xi.e.3x2+4y2=192 Hence, the correct answer is option A.

COURSES

EXAMS

CLASSES

EXAM PREPARATION

RESOURCES

COMPANY

FOLLOW US

FREE TEXTBOOK SOLUTIONS

STATE BOARDS

FOLLOW US

A point moves such that its distance from the point (4, 0) is half that of its distance from the line x = 16. the locus of the point is
(a) 3x² + 4y² = 192
(b) 4x² + 3y² = 192
(c) x² + y² = 12
(d) none of these