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

If $fraction numerator x over denominator a end fraction plus fraction numerator y over denominator b end fraction$ = 1 is a tangent to the curve x = 4t,y = $fraction numerator 4 over denominator t end fraction$ , t $element of$ R then -

a > 0 , b > 0
a > 0, b < 0
a < 0, b > 0
None of these

hint Hint:

Find slope i.e $fraction numerator d y over denominator d x end fraction$

The correct answer is: a > 0 , b > 0

Given : x = 4t, y = $fraction numerator 4 over denominator t end fraction$ , t $element of$ R
$rightwards double arrow x cross times space y space equals space k t space cross times k over t space equals space k squared$ , ( the curve is a rectangular parabola)
$rightwards double arrow fraction numerator x y 1 space plus space y x 1 over denominator 2 end fraction space equals space k squared rightwards double arrow x y 1 space plus y x 1 space equals space 2 k squared$
$rightwards double arrow space L e t space x 1 space equals space k t space a n d space y 1 space equals space k over t rightwards double arrow x cross times k over t space plus space y space cross times k t space equals space 2 k squared rightwards double arrow x over t space plus space t y space space equals space 2 k rightwards double arrow S l o p e space o f space tan g e n t space equals space fraction numerator negative space c o e f f e c i e n t space o f space x over denominator c o e f f e c i e n t space o f space y end fraction rightwards double arrow S l o p e space o f space tan g e n t space equals space fraction numerator begin display style bevelled fraction numerator negative 1 over denominator t end fraction end style over denominator t end fraction space equals fraction numerator negative 1 over denominator t squared end fraction less than space 0$
$rightwards double arrow x over a space plus space y over b space equals space 1 comma space i. e. space tan g e n t space f o r space x y space equals space k squared rightwards double arrow S l o p e space o f space tan g e n t space less than space 0 rightwards double arrow S l o p e space o f space l i n e space equals space fraction numerator begin display style bevelled fraction numerator negative 1 over denominator a end fraction end style over denominator begin display style bevelled 1 over b end style end fraction space less than space 0 rightwards double arrow S l o p e space o f space l i n e space equals space fraction numerator negative b over denominator a end fraction less than space 0 rightwards double arrow S l o p e space o f space l i n e space equals space b over a space greater than space 0 rightwards double arrow T h i s space i m p l i e s space e i t h e r space b space greater than space 0 space comma space a greater than space 0 space o r space b space less than 0 space space a n d space a less than space 0$

$fraction numerator d y over denominator d x end fraction space equals space fraction numerator begin display style bevelled fraction numerator d y over denominator d t end fraction end style over denominator begin display style bevelled fraction numerator d x over denominator d t end fraction end style end fraction fraction numerator d y over denominator d t end fraction space equals space 4 space a n d space space fraction numerator d x over denominator d t end fraction space equals negative space 4 over t squared S u b s t i t u t i n g space t h e space v a l u e s fraction numerator d y over denominator d x end fraction space equals space fraction numerator begin display style bevelled fraction numerator d y over denominator d t end fraction end style over denominator begin display style bevelled fraction numerator d x over denominator d t end fraction end style end fraction space equals space fraction numerator 4 over denominator begin display style bevelled fraction numerator negative 4 over denominator t squared end fraction end style end fraction space equals space minus 1 over t squared space$

Related Questions to study

The line $fraction numerator x over denominator a end fraction$ + $fraction numerator y over denominator b end fraction$ = 1 touches the curve $y space equals space b e to the power of negative x over a end exponent$ at the point :

The line $fraction numerator x over denominator a end fraction$ + $fraction numerator y over denominator b end fraction$ = 1 touches the curve $y space equals space b e to the power of negative x over a end exponent$ at the point :

An object moves in a straight line. It starts from the rest and its acceleration is . 2 ms².After reaching a certain point it comes back to the original point. In this movement its acceleration is -3 ms², till it comes to rest. The total time taken for the movement is 5 second. Calculate the maximum velocity.

An object moves in a straight line. It starts from the rest and its acceleration is . 2 ms².After reaching a certain point it comes back to the original point. In this movement its acceleration is -3 ms², till it comes to rest. The total time taken for the movement is 5 second. Calculate the maximum velocity.

For the ellipse $fraction numerator x to the power of 2 end exponent over denominator 2 end fraction plus fraction numerator y to the power of 2 end exponent over denominator 1 end fraction equals 1 comma$ the foci are

For the ellipse $fraction numerator x to the power of 2 end exponent over denominator 2 end fraction plus fraction numerator y to the power of 2 end exponent over denominator 1 end fraction equals 1 comma$ the foci are

parallel

For the ellipse $x squared over 4 plus y squared over 1 equals 1$ , the latus rectum is

For the ellipse $x squared over 4 plus y squared over 1 equals 1$ , the latus rectum is

The sum of distances of any point on the ellipse 3 x² + 4y² = 24 from its foci is

The sum of distances of any point on the ellipse 3 x² + 4y² = 24 from its foci is

The equations x = a $open parentheses fraction numerator 1 minus t to the power of 2 end exponent over denominator 1 plus t to the power of 2 end exponent end fraction close parentheses semicolon y equals fraction numerator 2 b t over denominator 1 plus t to the power of 2 end exponent end fraction semicolon t element of R$ represent

The equations x = a $open parentheses fraction numerator 1 minus t to the power of 2 end exponent over denominator 1 plus t to the power of 2 end exponent end fraction close parentheses semicolon y equals fraction numerator 2 b t over denominator 1 plus t to the power of 2 end exponent end fraction semicolon t element of R$ represent

parallel

The equations x = a cos q, y = b sin q, 0 ≤ q < 2 p, a ≠ b, represent

The equations x = a cos q, y = b sin q, 0 ≤ q < 2 p, a ≠ b, represent

The line y = 2x + c touches the ellipse $fraction numerator x to the power of 2 end exponent over denominator 16 end fraction plus fraction numerator y to the power of 2 end exponent over denominator 4 end fraction equals 1$ if c is equal to

The line y = 2x + c touches the ellipse $fraction numerator x to the power of 2 end exponent over denominator 16 end fraction plus fraction numerator y to the power of 2 end exponent over denominator 4 end fraction equals 1$ if c is equal to

The eccentricity of the conic 3x² + 4y² = 24 is

The eccentricity of the conic 3x² + 4y² = 24 is

parallel

The equation of the ellipse whose focus is (1, -1). directrix x – y – 3 = 0 and eccentricity $fraction numerator 1 over denominator 2 end fraction$ is

The equation of the ellipse whose focus is (1, -1). directrix x – y – 3 = 0 and eccentricity $fraction numerator 1 over denominator 2 end fraction$ is

The equation ax² + 2hxy + by² + 2gx + 2fy + c = 0 represents an ellipse if

The equation ax² + 2hxy + by² + 2gx + 2fy + c = 0 represents an ellipse if

On a new year day every student of a class sends a card to every other student. The postman delivers 600 cards. The number of students in the class are :

On a new year day every student of a class sends a card to every other student. The postman delivers 600 cards. The number of students in the class are :

parallel

A tangent to the ellipse x² + 4y² = 4 meets the ellipse x² + 2y² = 6 at P and Q. The angle between the tangents at P and Q of the ellipse x² + 2y² = 6 is

A tangent to the ellipse x² + 4y² = 4 meets the ellipse x² + 2y² = 6 at P and Q. The angle between the tangents at P and Q of the ellipse x² + 2y² = 6 is

An ellipse has OB as a semi – minor axis, F, F' are its foci and the angle FBF' is a right angle. Then the eccentricity of the ellipse is

An ellipse has OB as a semi – minor axis, F, F' are its foci and the angle FBF' is a right angle. Then the eccentricity of the ellipse is

The equation of the tangents drawn at the ends of the major axis of the ellipse 9x² + 5y² – 30y = 0 is

The equation of the tangents drawn at the ends of the major axis of the ellipse 9x² + 5y² – 30y = 0 is

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.