Maths-

General

Easy

Question

# Statement- (1) : PQ is a focal chord of a parabola. Then the tangent at P to the parabola is parallel to the normal at Q.

Statement- (2) : If P(t_{1}) and Q(t_{2}) are the ends of a focal chord of the parabola y^{2} = 4ax, then t_{1}t_{2} = –1.

- Both S
_{1} & S_{2} are correct & S_{2} is correct explanation of S_{1}
- Both S
_{1} & S_{2} are correct but S_{2} is not correct explanation of S_{1}
- S
_{1} is correct S_{2} is wrong
- S
_{1} is wrong S_{2} is correct

_{1}& S_{2}are correct & S_{2}is correct explanation of S_{1}_{1}& S_{2}are correct but S_{2}is not correct explanation of S_{1}_{1}is correct S_{2}is wrong_{1}is wrong S_{2}is correctHint:

### properties of tangent and normal of a parabola.

## The correct answer is: Both S_{1} & S_{2} are correct & S_{2} is correct explanation of S_{1}

Both S1 & S2 are correct & S2 is correct explanation of S1

equation of tangent at P : t_{1}y = x+at^{2}

equation of normal at Q : y+ xt_{2} = 2at_{2} + at_{2}^{3}

the slopes at P and Q are 1/t1 and -t2 respectively

slopes at the two extremeties of a focal chord are : (t,-1/t)

this property is used to explain the behaviour of tangents and normals at the respective points.

### Related Questions to study

maths-

### Statement- (1) : Let () and () are the ends of a focal chord of = 4x then

Statement- (2) : PSQ is the focal of a parabola with focus S and latus rectum then SP + SQ = 2.

### Statement- (1) : Let () and () are the ends of a focal chord of = 4x then

Statement- (2) : PSQ is the focal of a parabola with focus S and latus rectum then SP + SQ = 2.

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### Statement- (1) : If 4 & 3 are length of two focal segments of focal chord of parabola y^{2} = 4ax than latus rectum of parabola will be 48/7 units

Statement- (2) : If 1 & 2 are length of focal segments of focal chord than its latus rectum is .

### Statement- (1) : If 4 & 3 are length of two focal segments of focal chord of parabola y^{2} = 4ax than latus rectum of parabola will be 48/7 units

Statement- (2) : If 1 & 2 are length of focal segments of focal chord than its latus rectum is .

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### The current i in an inductance coil varies with time, t according to the graph shown in fig. Which one of the following plots shows the variation of voltage in the coil with time

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### Figure (i) shows a conducting loop being pulled out of a magnetic field with a speed v. Which of the four plots shown in figure (ii) may represent the power delivered by the pulling agent as a function of the speed v

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### The graph gives the magnitude B(t) of a uniform magnetic field that exists throughout a conducting loop, perpendicular to the plane of the loop. Rank the five regions of the graph according to the magnitude of the emf induced in the loop, greatest first

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### Some magnetic flux is changed from a coil of resistance 10 ohm. As a result an induced current is developed in it, which varies with time as shown in figure. The magnitude of change in flux through the coil in webers is

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### A horizontal loop abcd is moved across the pole pieces of a magnet as shown in fig. with a constant speed v. When the edge ab of the loop enters the pole pieces at time t = 0 sec. Which one of the following graphs represents correctly the induced emf in the coil

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### An alternating current of frequency 200 rad/sec and peak value 1A as shown in the figure, is applied to the primary of a transformer. If the coefficient of mutual induction between the primary and the secondary is 1.5 H, the voltage induced in the secondary will be

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Statement (2): Two perpendicular tangents of a parabola, always meets on axis.

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Statement (2): Two perpendicular tangents of a parabola, always meets on axis.

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Statement (2): A parabola is symmetric about it’s axis.

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Statement (2): A parabola is symmetric about it’s axis.

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### y^{2} = 4x is the equation of a parabola.

Assertion : Through ( + 1), 3 normals can be drawn to the parabola, if < 2

Reason : The point ( + 1) lies outside the parabola for all –1.

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Assertion : Through ( + 1), 3 normals can be drawn to the parabola, if < 2

Reason : The point ( + 1) lies outside the parabola for all –1.

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Reason (R) : The tangents at point P and Q on parabola meet in T, then ST^{2} = SP. SQ.

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Reason (R) : The tangents at point P and Q on parabola meet in T, then ST^{2} = SP. SQ.

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### The variation of induced emf (E) with time (t) in a coil if a short bar magnet is moved along its axis with a constant velocity is best represented as

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