The Vertex Of A Parabola Is The Point (a, B) And Latus-rectum Is Of Length l. If The Axis Of The Parabola Is Along The Positive Direction Of Y-axis. Then Its Equation Is

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Question

The vertex of a parabola is the point (a, b) and latus-rectum is of length l. If the axis of the parabola is along the positive direction of y-axis. Then its equation is

Solution

Correct option is

The equation of the parabola referred to its vertex as the origin

X2 = ly, where x = X + a, y = Y + b. Therefore the equation of the parabola referred to the point (a, b) as the vertex is

(x – a)2 = l(y – b) or .

Testing

SIMILAR QUESTIONS

Q1

If the line 2x + 3y = 1 touch the parabola y2 = 4ax at the pointP. Find the focal distance of the point P.

Q2

Find the angle between the tangents of the parabola y2 = 8x, which are drawn from the point (2, 5).

Q3

Find the locus of middle point of chord y2 = 4ax drawn through vertex.

Q4

Find the locus of the mid-point of the chords of the parabola y2 = 4ax which subtend a right angle at the vertex of the parabola.

Q5

Show that the normal at a point (at2, 2at) on the parabola y2 = 2ax cuts the curve again at the point whose parameter .

Q6

Show that the normal at a point (at2, 2at) on the parabola y2 = 2ax cuts the curve again at the point whose parameter .

Q7

Find the locus of a pint P which moves such that two of the three normal’s drawn from it to the parabola y2 = 4ax are mutually perpendicular.

Q8

If normal at the point (at2, 2at) in the parabola y2 = 4axintersects the parabola again at the (am2, 2am), then find the minimum value of m2.

Q9

The equation of circle touching the parabola y2 = 4x at the point  (1, –2) and passing through origin is

Q10

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