Question

The curve described parametrically by x = t2 + t + 1, y = t2 – + 1 represents.

Solution

Correct option is

A parabola

 

Eliminating t, 2(x + y) = (x – y)2 + 4

Since 2nd degree terms form a perfect square, it represents a parabola.

SIMILAR QUESTIONS

Q1

Slope of common tangent to parabolas y2 = 4x and x2 = 8y is

Q2

If a focal chord with positive slope of the parabola y2 = 16xtouches the circle x2 + y2 – 12+ 34 = 0, then m is

Q3

If 2y = x + 24 is a tangent to parabola y2 = 24x, then its distance from parallel normal is

Q4

PQ is a focal chord of the parabola y2 = 4axO is the origin. Find the coordinates of the centroid, G, of triangle OPQ and hence find the locus of G as PQ varies.

Q5

Find the shortest distance between the circle x2 + y2 – 24y + 128 = 0 and the parabola y2 = 4x.

Q6

The equation of the directrix of the parabola y2 + 4y + 4x + 2 = 0 is  

Q7

If the line x – 1 = 0 is the directrix of the parabola y– ky + 8 = 0, then one of the of the value of k is

  

Q8

Equation of the parabola whose axis is y = x distance from origin to vertex is  and distance form origin to focus is , is (Focus and vertex lie in Ist quadrant) :

Q9

The focal chord of y2 = 16x is tangent to (x – 6)2 + y2 = 2, then the possible values of the slope of this chord, are

Q10

The locus of the mid-point of the line segment joining the focus to a moving point on the parabola y2 = 4ax is another parabola with directrix