Equation of Normal When Slope Is Given
Trending Questions
Q. If the parabolas y2=4b(x−c) and y2=8ax have a common normal, then which one of the follwing is a valid choice for the ordered triplets (a, b, c)?
- (12, 2, 0)
- (1, 1, 0)
- (1, 1, 3)
- (12, 2, 3)
Q. If 2x+y+k=0 is a normal to the parabola y2=−8x, then the value of k is
Q. Shortest distance (in units) between the two parabolas y2=x−2, x2=y−2 is
- 14√2
- 54√2
- 72√2
- 67√2
Q. The line y = 2x + k is a normal to the parabola y2=4x then k =
- -12
- 10
- -10
- 12
Q. If the normal at the point P(ap2, 2ap) meets the parabola at Q(aq2, 2aq) such that the lines joining the origin to P and Q are at right angle, then
- p2=2
- pq−4=0
- pq+4=0
- p2=4
Q. If the sum of the slopes of the normal from a point P to the hyperbola xy=c2 is equal to λ(λ∈R+), then the locus of the point P is
- x2=λc2
- y2=λc2
- xy=λc2
- x2−y2=λc2
Q. The equation of the line of the shortest distance between the parabola y2=4x and the circle x2+y2−4x−2y+4=0
- x+y=3
- x-y=3
- 2x+y=5
- done
Q. F is the family of curves in the XY plane., given by y=x+ce−x, where c ∈ R is an arbitrary constant. The orthogonal trajectories of the curve of the family F forms the family F′. Then which of the following statement(s) is\are TRUE for F′.
- xey=ey(y−2)+c, is general solution for F′
- x=y−2 is a particular solution for F′
- If F′ passes through (4, 0), then F′ is x=(y−2)+6ey
- xe=e(y−2)+c, is general solution for F′
Q. The equation of the normals at the end points of the latus rectum of the parabola y2=8x is/are
- x+y+6=0
- x−y+6=0
- x−y−6=0
- x+y−6=0
Q.
If a circle and rectangular hyperbola xy = c2 meets in 4 points P , Q , R and S then OP2 + OQ2 + OR2 + OS2=______ where r is the radius of the circle. O is the origin.
Q. The line x+2y=36 is normal to the parabola x2=12y at the point whose distance from the focus of the parabola is
Q. A parabolic mirror is kept along y2=4x. A ray along y=3 strikes the mirror (from the positive direction of x−axis) and gets reflected along the line L=0. Then which of the following is NOT true ?
- The line L=0 passes through (0, −125).
- The line L=0 intersects the x−axis at (1, 0).
- The line L=0 is a tangent to the circle x2+y2=1.
- The line L=0 makes acute angle with positive x−axis in anticlockwise direction.
Q. Shortest distance between the line y−x=1 and the curve x=y2 is
- √34
- 3√28
- 3√25
- 2√38
Q. Let O be the origin and A be a point on the curve y2=4x Then the locus of the midpoint of OA is
Q. The maximum possible area bounded by the parabola y=x2+x+10 and a chord of the parabola of length 1 is.
- 16
- 13
- 12
- 112
Q.
The foci of the conjugate hyperbola of the hyberbola x24−y212=1