Multiple Choice Questions:

Problem 1:

A line bisecting the ordinate PN of a point P , , on the parabola is drawn parallel to the axis to meet the curve at Q. If NQ meets the tangent at the vertex at the point T, then the coordinates of T are

(a) (b) Slatex (0,2at)$ (c) (d)

Problem 2:

If P, Q, R are three points on a parabola whose ordinates are in geometrical progression, then the tangents at P and R meet on

(a) the line through Q parallel to x-axis

(b) the line through Q parallel to y-axis

(c) the line through Q to the vertex

(d) the line through Q to the focus.

Problem 3:

The locus of the midpoint of the line segment joining the focus to a moving point on the parabola is another parabola with directrix:

(a) (b) (c) (d)

Problem 4:

Equation of the locus of the pole with respect to the ellipse , of any tangent line to the auxiliary circle is the curve where

(a) (b) (c) (d)

Problem 5:

The locus of the points of the intersection of the tangents at the extremities of the chords of the ellipse , which touch the ellipse is

(a) (b) (c) (d) none of these.

Problem 6:

If an ellipse slides between two perpendicular straight lines, then the locus of its centre is

(a) a parabola (b) an ellipse (c) a hyperbola (d) a circle

Problem 7:

Let and where , be two points on the hyperbola . If is the point of intersection of normals at P and Q, then k is equal to

(a) (b) (c) (d)

Problem 8:

A straight line touches the rectangular hyperbola , and the parabola . An equation of the line is

(a) (b) (c) (d)

*There could be multiple answers to this question.*

Problem 9:

Two parabolas C and D intersect at the two different points, where C is and D is . The intersection at which the x-value is positive is designated point A, and at this intersection. The tangent line l at A to the curve D intersects curve C at point B, other than A. If x-value of point B is 1(one), then what is a equal to?

Problem 10:

The triangle formed by the tangent to the parabola at the point whose abscissa is , the y-axis and the straight line has the greatest area if . Fill in the question mark!

More later,

*Nalin Pithwa.*

PS: I think let’s continue this focus on co-ordinate geometry of IITJEE Mains Maths for some more time.

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