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Maths-

General

Easy

Question

The normals to the curve x = a ( $theta$ + sin $theta$ ), y = a (1 – cos $theta$ ) at the points $theta$ = (2n + 1) $pi$ , n $element of$ I are all -

parallel to x-axis
parallel to y-axis
parallel to the line y = x
None of these

The correct answer is: parallel to x-axis

Related Questions to study

The normal to the curve x = 3 cos $theta$ – $cos cubed theta$ , y = 3 sin $theta$ – $sin cubed$ $theta$ at the point $theta$ = $pi$ /4 passes through the point -

The normal to the curve x = 3 cos $theta$ – $cos cubed theta$ , y = 3 sin $theta$ – $sin cubed$ $theta$ at the point $theta$ = $pi$ /4 passes through the point -

The normal of the curve given by the equation x = a (sin $theta$ + cos $theta$ ), y = a (sin $theta$ – cos $theta$ ) at the point Q is -

The normal of the curve given by the equation x = a (sin $theta$ + cos $theta$ ), y = a (sin $theta$ – cos $theta$ ) at the point Q is -

If the tangent at ‘t’ on the curve y = $8 t cubed space minus 1$ , x = $4 t squared space plus space 3$ meets the curve again at $t subscript 1$ and is normal to the curve at that point, then value of t must be -

If the tangent at ‘t’ on the curve y = $8 t cubed space minus 1$ , x = $4 t squared space plus space 3$ meets the curve again at $t subscript 1$ and is normal to the curve at that point, then value of t must be -

parallel

The tangent at ( $t$ , $t squared$ – $t cubed$ ) on the curve y = $x squared$ – $x cubed$ meets the curve again at Q, then abscissa of Q must be -

The tangent at ( $t$ , $t squared$ – $t cubed$ ) on the curve y = $x squared$ – $x cubed$ meets the curve again at Q, then abscissa of Q must be -

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 -

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 -

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 :

parallel

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

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

parallel

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

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

parallel

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

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

parallel

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