Have a query? Ask a Tutor!!

Access to best educators and exclusive paper discussions

Offsite Campus Turito Championship

Can’t find what you’re looking for?

Our tutors are from top schools around the world, and they are waiting for you 24/7, anytime, anywhere.

Homework- One to One Solutions
Understand concepts to solve better
Get your doubts solved instantly

Maths-

General

Easy

Question

The number of values of $c$ such that the straight line y=4x+c touches the curve $left parenthesis x to the power of 2 end exponent divided by 4 right parenthesis plus y to the power of 2 end exponent equals 1$ is‐

$0$
1
2
infinite

The correct answer is: 2

We need to find the number of values of $c$ such that the straight line y=4x+c touches the curve $left parenthesis x to the power of 2 end exponent divided by 4 right parenthesis plus y to the power of 2 end exponent equals 1$ .
$S i n c e space t h e space l i n e space y equals 4 x plus c space t o u c h e s space t h e space e l l i p s e fraction numerator space x squared over denominator 4 end fraction plus y squared equals 1 comma space w e space s u b s t i t u t e space y space a s space 4 x plus c space i n t o space t h e space e l l i p s e. W e space g e t space fraction numerator space x squared over denominator 4 end fraction plus 16 space x squared plus space 8 c x plus c squared equals 1 space x squared plus 64 space x squared plus 32 c x plus 4 c squared minus 4 equals 0 T h e space d i s c r i m i n a n t space o f space t h i s space q u a d r a t i c space s h o u l d space b e space z e r o space sin c e space w e space h a v e space o n l y space o n e space v a l u e space o f space x. open parentheses 32 c close parentheses squared equals 4 cross times 65 cross times left parenthesis 4 c squared minus 4 right parenthesis 1024 c squared equals 16 cross times 65 cross times left parenthesis c squared minus 1 right parenthesis 64 c squared equals 65 cross times left parenthesis c squared minus 1 right parenthesis 64 c squared equals 65 c squared minus 65 c squared equals 65 T h u s comma space w e space h a v e space t w o space v a l u e s space o f space c.$

Therefore, there are two values of c.

Related Questions to study

Let P be any point on any directrix of an ellipse Then the chords of contact of point P with respect to the ellipse and its auxiliary circle intersect at

Let P be any point on any directrix of an ellipse Then the chords of contact of point P with respect to the ellipse and its auxiliary circle intersect at

An ellipse having foci at (3, 3) and (-4,4) and passing through the origin has eccentricity equal to‐

An ellipse having foci at (3, 3) and (-4,4) and passing through the origin has eccentricity equal to‐

Normals $A O comma A A subscript 1 end subscript comma A A subscript 2 end subscript$ are drawn to parabola $y to the power of 2 end exponent equals 8 x$ from the pointA (h, 0) If triangle $O A subscript 1 end subscript A subscript 2 end subscript$ ( $O$ being the origin) is equilateral, then possible value of h’ is

Normals $A O comma A A subscript 1 end subscript comma A A subscript 2 end subscript$ are drawn to parabola $y to the power of 2 end exponent equals 8 x$ from the pointA (h, 0) If triangle $O A subscript 1 end subscript A subscript 2 end subscript$ ( $O$ being the origin) is equilateral, then possible value of h’ is

parallel

Given: A circle, $2 x to the power of 2 end exponent plus 2 y to the power of 2 end exponent equals 5$ and a parabola, $y to the power of 2 end exponent equals 4 square root of 5 x$
Statement‐I:: An equation of a common tangent to these curves is $y equals x plus square root of 5.$
Statement‐II:: If the line, $y equals m x plus fraction numerator square root of 5 over denominator m end fraction left parenthesis m not equal to 0 right parenthesis$ is their common tangent, then $m$ satisfies $m to the power of 4 end exponent minus 3 m to the power of 2 end exponent plus 2 equals 0.$

Given: A circle, $2 x to the power of 2 end exponent plus 2 y to the power of 2 end exponent equals 5$ and a parabola, $y to the power of 2 end exponent equals 4 square root of 5 x$
Statement‐I:: An equation of a common tangent to these curves is $y equals x plus square root of 5.$
Statement‐II:: If the line, $y equals m x plus fraction numerator square root of 5 over denominator m end fraction left parenthesis m not equal to 0 right parenthesis$ is their common tangent, then $m$ satisfies $m to the power of 4 end exponent minus 3 m to the power of 2 end exponent plus 2 equals 0.$

In any equilateral $capital delta$ , three circles of radii one are touching to the sides given as in the figure then area of the $capital delta$ is

In any equilateral $capital delta$ , three circles of radii one are touching to the sides given as in the figure then area of the $capital delta$ is

If the sides a, b, c of a triangle are such that a : b : c : : 1 : $square root of 3$ : 2, then the A : B : C is -

If the sides a, b, c of a triangle are such that a : b : c : : 1 : $square root of 3$ : 2, then the A : B : C is -

parallel

A block placed on a rough inclined plane of inclination ( $theta$ =30°) can just be pushed upwards by applying a force "F" as shown. If the angle of inclination of the inclined plane is increased to ( $theta$ = 60°), the same block can just be prevented from sliding down by application of a force of same magnitude. The coefficient of friction between the block and the inclined plane is

A block placed on a rough inclined plane of inclination ( $theta$ =30°) can just be pushed upwards by applying a force "F" as shown. If the angle of inclination of the inclined plane is increased to ( $theta$ = 60°), the same block can just be prevented from sliding down by application of a force of same magnitude. The coefficient of friction between the block and the inclined plane is

physics-General

The tube AC forms a quarter circle in a vertical plane. The ball B has an area of cross–section slightly smaller than that of the tube, and can move without friction through it. B is placed at A and displaced slightly. It will

The tube AC forms a quarter circle in a vertical plane. The ball B has an area of cross–section slightly smaller than that of the tube, and can move without friction through it. B is placed at A and displaced slightly. It will

physics-General

A small cube with mass M starts at rest at point 1 at a height 4R, where R is the radius of the circular part of the track. The cube slides down the frictionless track and around the loop. The force that the track exerts on the cube at point 2 is nearly _____ times the cube's weight Mg.

A small cube with mass M starts at rest at point 1 at a height 4R, where R is the radius of the circular part of the track. The cube slides down the frictionless track and around the loop. The force that the track exerts on the cube at point 2 is nearly _____ times the cube's weight Mg.

physics-General

parallel

A bob attached to a string is held horizontal and released. The tension and vertical distance from point of suspension can be represented by.

A bob attached to a string is held horizontal and released. The tension and vertical distance from point of suspension can be represented by.

physics-General

A ball whose size is slightly smaller than width of the tube of radius 2.5 m is projected from bottommost point of a smooth tube fixed in a vertical plane with velocity of 10 m/s. If N₁ and N₂ are the normal reactions exerted by inner side and outer side of the tube on the ball

A ball whose size is slightly smaller than width of the tube of radius 2.5 m is projected from bottommost point of a smooth tube fixed in a vertical plane with velocity of 10 m/s. If N₁ and N₂ are the normal reactions exerted by inner side and outer side of the tube on the ball

physics-General

A block of mass m moving with a velocity v₀ on a smooth horizontal surface strikes and compresses a spring of stiffness k till mass comes to rest as shown in the figure. This phenomenon is observed by two observers:
A: standing on the horizontal surface
B: standing on the block

According to observer B, the potential energy of the spring increases

A block of mass m moving with a velocity v₀ on a smooth horizontal surface strikes and compresses a spring of stiffness k till mass comes to rest as shown in the figure. This phenomenon is observed by two observers:
A: standing on the horizontal surface
B: standing on the block

According to observer B, the potential energy of the spring increases

physics-General

parallel

A block of mass m moving with a velocity v0 on a smooth horizontal surface strikes and compresses a spring of stiffness k till mass comes to rest as shown in the figure. This phenomenon is observed by two observers:
A: standing on the horizontal surface
B: standing on the block

To an observer B, when the block is compressing the spring

A block of mass m moving with a velocity v0 on a smooth horizontal surface strikes and compresses a spring of stiffness k till mass comes to rest as shown in the figure. This phenomenon is observed by two observers:
A: standing on the horizontal surface
B: standing on the block

To an observer B, when the block is compressing the spring

physics-General

A block of mass m moving with a velocity v₀ on a smooth horizontal surface strikes and compresses a spring of stiffness k till mass comes to rest as shown in the figure. This phenomenon is observed by two observers:
A: standing on the horizontal surface
B: standing on the block

According to the observer A

A block of mass m moving with a velocity v₀ on a smooth horizontal surface strikes and compresses a spring of stiffness k till mass comes to rest as shown in the figure. This phenomenon is observed by two observers:
A: standing on the horizontal surface
B: standing on the block

According to the observer A

physics-General

A block of mass m moving with a velocity v0 on a smooth horizontal surface strikes and compresses a spring of stiffness k till mass comes to rest as shown in the figure. This phenomenon is observed by two observers:
A: standing on the horizontal surface
B: standing on the block

To an observer A, the net work done on the block is

A block of mass m moving with a velocity v0 on a smooth horizontal surface strikes and compresses a spring of stiffness k till mass comes to rest as shown in the figure. This phenomenon is observed by two observers:
A: standing on the horizontal surface
B: standing on the block

To an observer A, the net work done on the block is

physics-General

parallel

card img

With Turito Academy.

card img

With Turito Foundation.

card img

Get an Expert Advice From Turito.

Turito Academy

card img

With Turito Academy.

Test Prep

card img

With Turito Foundation.