# Equation of Normal at Given Point

## Trending Questions

**Q.**The length of normal chord of parabola y2=4x, which subtends an angle of 90∘ at the vertex is

- 8√3 units
- 6√3 units
- 7√2 units
- 9√2 units

**Q.**Let P be the point on the parabola y2=4x which is at the shortest distance from the centre S of the circle x2+y2–4x–16y+64=0. Let Q be the point on the circle dividing the line segment SP internally. Then

- SP=2√5
- SQ:QP=(√5+1):2
- the x-intercept of the normal to the parabola at P is 6
- the slope of the tangent to the circle at Q is 12

**Q.**The normal to the parabola y2=8x at the point (2, 4) meets the parabola again at the point _____.

- (18, -12)
- (-18, 12)
- (18, 12)
- (-18, -12)

**Q.**

The distance of the point $\left(1,2\right)$ from the line $x+y+5=0$ measured along the line parallel to $3x-y=7$ is equal to

$4\sqrt{10}$

$40$

$\sqrt{40}$

$10\sqrt{2}$

**Q.**If the normals of the parabola y2=4x drawn at the end points of its latus rectum are tangents to the circle (x−3)2+(y+2)2=r2, then the value of r2 is

**Q.**The tangents and normals at the ends of the latus rectum of a parabola forms a

- square
- parallelogram
- rectangle
- rhombus

**Q.**If the tangents and normals at the extremities of a focal chord of any standard parabola intersect at S≡(x1, y1) and R≡(x2, y2) respectively, then

- If the equation of parabola is y2=±4ax, then y1=y2
- If the equation of parabola is x2=±4ay, then x1=x2
- the circle with focal chord as diameter will always pass through the points R and S
- the circle with RS as diameter will always pass through extemities of focal chord

**Q.**Two tangents are drawn to the parabola y2=8x which meets the tangent at vertex at P and Q respectively. If PQ=4 units, then the locus of the point of intersection of the two tangents is

- x2=8(y+2)
- x2=8(y−2)
- y2=8(x−2)
- y2=8(x+2)

**Q.**Let AB is a normal chord of parabola y2=4x, with foot of normal as A(1, −2). If AB=p√q, where p is a natural number and q is a prime number, then pq is equal to

**Q.**

What angle has a tangent of $2$?

**Q.**

The chord AB of the parabola y2=4ax cuts the axis of the parabola at C. If A=(at21, 2at1), B=(at22, 2at2) and AC : AB = 1:3 then

None of these

t2=2t1

t2+2t1=0

t1+2t2=0

**Q.**If the tangents drawn from a point to the parabola y2=4ax are also normals to the parabola x2=4by, then

- b2≥8a2
- b2≥2a2
- a2≥2b2
- a2≥8b2

**Q.**If PQ is a normal chord of the parabola y2=4ax at P(at2, 2at). Then the axis of the parabola divides ¯¯¯¯¯¯¯¯PQ in the ratio

- t2t2+2
- t2t2−2
- 2t2t2−2
- t22(t2−2)

**Q.**Consider a parabola y2=4ax. If the normal to the parabola at the point (at2, 2at) cuts the parabola again at (aT2, 2aT), then

- T2≥8
- T2≤6
- T∈(−8, 8)
- T∈(−∞, −8)∪(8, ∞)

**Q.**Length of normal chord of parabola y2=4x which makes an inclination of π4 with the positive direction of x−axis is

- 8 units
- 8√2 units
- 4 units
- 4√2 units

**Q.**If y=x√2−8√2 is a normal chord to y2=8x.Then its length (in units) is

- 12√3
- 2√3
- 16√3
- 4√3

**Q.**If normals drawn to y2=12x makes an angle of 45° with x−axis, then foot of the normals is/are

- (12, −12)
- (12, 12)
- (3, −6)
- (3, 6)

**Q.**P and Q are two distinct points on the parabola, y2=4x, with parameters t and t1 respectively. If the normal at P passes through Q, then the minimum value of t21 is:

- 8
- 6
- 2
- 4

**Q.**The normal chord of a parabola y2=4ax at a point whose ordinate is equal to abscissa, subtends a right angle at

- focus
- vertex
- ends of the latusrectum
- any point on directrix

**Q.**If the normal at point (1, 2) on the parabola y2=4x meets the parabola again a point (t2, 2t), then the value of t is

- 1
- −1
- −3
- 3

**Q.**The normal at P(2, 4) to y2=8x meets the parabola at Q. Then the equation of the circle having normal chord PQ as diameter is

- x2+y2−20x+8y−12=0
- x2+y2−10x+4y−8=0
- x2+y2−12x+6y−15=0
- x2+y2−10x+8y−12=0

**Q.**Locus of a point through which three normals of parabola y2=4ax are passing, two of which are making angles α and β with positive x− axis and tanα⋅tanβ=2 is

- y(y2−2ax)=0
- y(y2+2ax)=0
- y(y2−4ax)=0
- y(y2−ax)=0

**Q.**Let PQ be a chord of the parabola y2=8x. A circle drawn with PQ as diameter passes through the vertex V of the parabola. If area of ΔPVQ=80 square unit, then the coordinates of P are

- (32, −16)
- (−32, 16)
- (−32, −16)
- (32, 16)

**Q.**The locus of the mid-points of the portion of the normal to the parabola y2=16x intercepted between the curve and the axis is another parabola whose latus rectum is

**Q.**If P and Q are the points of contact of tangents drawn from the point T to y2=4ax and PQ be a normal of the parabola at P, then the locus of the point which bisects TP is

- x+a=0
- x=1
- x+2a=0
- x=0

**Q.**

Find the equation of normal to the parabola

y2=16x at point (4, 8)

x + y + 4 = 0

x + y - 2 = 0

x + y - 3 = 0

x + y - 4 = 0

**Q.**If ax+by=1 is a tangent to the hyperbola x2a2−y2b2=1, then the value of a2–b2 is

- b2e2
- 1b2e2
- a2e2
- 1a2e2

**Q.**If the minimum distance between the parabolas y2−4x−8y+40=0 and x2−8x−4y+40=0 is d, then the value of d2 is

**Q.**If a point P on the axis of the parabola y2=4x is taken such that the point is at shortest distance from the circle x2+y2+2x−2√2y+2=0.Common tangents are drawn to the circle and the parabola from P.If the area of the ΔPAB is √a sq. units where A and B are the points of contact on two distinct tangents from P on circle and parabola respectively, then a=

**Q.**

Obtain the equation of hyperbola whose equations of asymptotes are x + 2y + 3 = 0 and 3x + 4y + 5 = 0 and hyperbola passes through (1, -1).