Question

Find the equation of the curve 2x2 + y2 – 3+ 5– 8 = 0 when the origin is transferred to the point (–1, 2) without changing the direction of axes.

Solution

Correct option is

2x2 + y2 – 7+ 9+ 11 = 0

Here we want to shift the origin to the point (–1, 2) without changing the direction of axes. Then we replace by – 1 and by + 2 in the equation of given curve then the transformed equation is:-

2 (– 1)2 + (+ 2)2 – 3 (– 1) + 5 (+ 2) – 8 = 0

⇒                                2x2 + y2 – 7+ 9+ 11 = 0

SIMILAR QUESTIONS

Q1

The number of points (p, q) such that p, q Ïµ {1, 2, 3, 4} and the equation px2 + qx + 1 = 0 has real roots is

Q2

If G is the centroid and I the incentre of the triangle with vertices A(–36, 7), B(20, 7) and C(0, –8), then GI is equal to

Q3

Consider the point   then

Q4

A variable straight line of slope 4 intersects the hyperbola xy = 1 at two points. The locus of the point which divides the line segment between these two points in the ratio 1 : 2 is

Q5

Find the co – ordinates of the point which divides the line segment joining the pints (5, – 2) and (9, 6) in the ratio 3 : 1.

Q6

Find the co – ordinates of a point which divides externally the line joining (1, 3) and (3, 9) in the ratio 1 : 3.

Q7

Two vertices of a triangle are (–1, 4) and (5, 2). If its centroid is (0, –3), find the third vertex.

Q8

Find the area of the pentagon whose vertices are A(1, 1), B(7, 21), C(7, –3), D(12, 2) and (0, –3).

Q9

Find the locus of a point which moves such that its distance from the point (0, 0) is twice its distance from the – axis.

Q10

Given the equation  through what angle should the axes be rotated so that the term in xy be waiting from the transformed equation.