Parametric Form of Normal : Ellipse
Trending Questions
Q. The line lx + my + n = 0 will be a normal to the hyperbola b2x2−a2y2=a2b2, if
- None of these
Q. The normal at P(θ) and D(θ+π2) meet the major axis of x2a2+y2b2=1 at Q and R. Then PQ2+DR2=
Q. If the normal at θ on the ellipse 5x2+14y2=70 cuts the curve again at a point 2θ, then cosθ =
Q.
The normal at a point P on the ellipse x2+4y2=16 meets the X - axis at Q. If M is the mid-point of the line segment PQ, then the locus of M intersects the latusrectum of the given ellipse at the points
(±3√52, ±27)
(±2√3, ±4√37)
(±3√52, ±√194)
(±2√3, ±17)
Q. If the normal to the ellipse 3x2+4y2=12 at a point P on it is parallel to the line, 2x+y=4 and the tangent to the ellipse at P passes through Q(4, 4) then PQ is equal to
- 5√52 unit
- √1572 unit
- √2212 unit
- √612 unit
Q. If the normal at any point P on the ellipse x29+y216=1 meets the axes at G and g, respectively, then the ratio of PG:Pg is
- 3:4
- 4:3
- 9:16
- 16:9
Q. If the tangent drawn at point P(t2, 2t) on the parabola y2=4x is same as the normal drawn at point Q(√5cosθ, 2sinθ) on the ellipse 4x2+5y2=20, then
- Q≡(−1, 4√5)
- Q≡(−1, −4√5)
- P≡(15, −2√5)
- P≡(15, 2√5)
Q. Which of the following is/are true ?
- There are infinite positive integral values of a for which (13x−1)2+(13y−2)2=(5x+12y−1a)2 represents an ellipse
- The minimum distance of a point (1, 2) from the ellipse 4x2+9y2+8x−36y+4=0 is 1 unit
- If from a point P(0, α) two normals other than axes are drawn to the ellipse x225+y216=1, then |α|<94
- If the length of latus rectum of an ellipse is one-third of its major axis, then its eccentricity is equal to 1√3
Q. Sum of distance's from the x−axis to the point(s) on the ellipse x29+y24=1, where the normal is parallel to the line 2x+y=1, is k5 unit, then k=
Q. The eccentricity of an ellipse whose centre is at the origin is 12. If one of its directrices is x=−4, then the equation of the normal to it at (1, 32) is:
- 2y−x=2
- 4x−2y=1
- 4x+2y=7
- x+2y=4