Tangents and Normals - Rajasthan Board (RBSE) STD 12 Science MATHS Questions

Q 1M.C.Q (1 Marks)1 Mark

The point on the curve $y^2 = x$ where tangent makes $45^\circ $ angle with $x-$ axis is :

A
$\Big(\frac{1}{2},\frac{1}{4}\Big)$
✓
$\Big(\frac{1}{4},\frac{1}{2}\Big)$
C
$(4, 2)$
D
$(1, 1)$

Answer: B.

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Q 2M.C.Q (1 Marks)1 Mark

The point on the curve $y^2 = x$ where tangent makes $45^\circ $ angle with $x-$ axis is :

A
$\Big(\frac{1}{2},\frac{1}{4}\Big)$
✓
$\Big(\frac{1}{4},\frac{1}{2}\Big)$
C
$(4,2)$
D
$(1,1)$

Answer: B.

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Q 3M.C.Q (1 Marks)1 Mark

The point on the curve $y = x^2 - 3x + 2$ where tangent is perpendicular to $y = x$ is :

A
$(0, 2)$
✓
$(1, 0)$
C
$(-1, 6)$
D
$(2, -2)$

Answer: B.

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Q 4M.C.Q (1 Marks)1 Mark

At what point the slope of the tangent to the curve $x^2 + y^2 - 2x - 3 = 0$ is zero :

A
$(3, 0), (-1, 0)$
B
$(3, 0), (1, 2)$
C
$(-1, 0), (1, 2)$
✓
$(1, 2), (1, -2)$

Answer: D.

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Q 5M.C.Q (1 Marks)1 Mark

The normal at the point $(1, 1)$ on the curve $2y + x^2 = 3$ is :

A
$x + y = 0$
✓
$x - y = 0$
C
$x + y + 1 = 0$
D
$x - y = 1$

Answer: B.

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Q 62 Marks Questions2 Marks

Write the value of $\Big(\frac{\text{dy}}{\text{dx}}\Big),$ if the normal to the curve y = f(x) at (x, y) is parallel to y-axis.

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Q 72 Marks Questions2 Marks

If the tangent to a curve at a point (x, y) is equally inclined to the co-ordinates axes then write the value of $\frac{\text{dy}}{\text{dx}}.$

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Q 82 Marks Questions2 Marks

Write the equation of the tangent drawn to the curve $\text{y}=\sin\text{x}$ at the point (0, 0).

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Q 92 Marks Questions2 Marks

Write the slop of the normal to the curve $\text{y}=\frac{1}{\text{x}}$ at the point $\Big(3,\frac{1}{3}\Big).$

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Q 102 Marks Questions2 Marks

If the tangent line at a point (x, y) on the curve y = f(x) is parallel to y-axis, find the value of $\frac{\text{dy}}{\text{dx}}.$

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Q 113 Marks Question3 Marks

Find the point on the curve $y = x^2$ where the slope of the tangent is equal to the x-coordinate of the point.

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Q 123 Marks Question3 Marks

Write the coordinates of the point at which the tangent to the curve $y = 2x^2 - x + 1$ is parallel to the line $y = 3x + 9$.

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Q 133 Marks Question3 Marks

Find the equation of the tangent to the curve $\sqrt{\text{x}}+\sqrt{\text{y}}=\text{a},$ at the point $\Big(\frac{\text{a}^2}{4},\frac{\text{a}^2}{4}\Big).$

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Q 143 Marks Question3 Marks

Write the angle between the curves $y = e^{-x}$ and $y = e^x$ at their point of intersections.

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Q 153 Marks Question3 Marks

Find the slope of the normal at the point 't' on the curve $\text{x}=\frac{1}{\text{t}},\text{y}=\text{t}.$

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Q 165 Marks Questions5 Marks

Find the equation of the tangent to the curve $\text{x}=\theta+\sin\theta,\text{y}+\cos\theta\text{ at }\theta=\frac{\pi}{4}.$

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Q 175 Marks Questions5 Marks

Show that the curve $\frac{\text{x}^2}{\text{a}^2+\lambda_1}+\frac{\text{y}^2}{\text{b}^2+\lambda_1}=1$ and $\frac{\text{x}^2}{\text{a}^2+\lambda_2}+\frac{\text{y}^2}{\text{b}^2+\lambda_2}=1$ intersect at right angles.

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Q 185 Marks Questions5 Marks

Find a point on the curve $y = x^3 - 3x$ where the tangent is parallel to the chord joining $(1, -2)$ and $(2, 2).$

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Q 195 Marks Questions5 Marks

Find the equations of the tangent and the normal to the following curves at the indicated points.
$\text{x}=\theta+\sin\theta,\text{y}=1+\cos\theta\text{ at }\theta=\frac{\pi}{2}$

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Q 205 Marks Questions5 Marks

Find the equation of the tangent line to the curve $y = x^2 - 2x + 7$ which is perpendicular to the line $5y - 15x = 13.$

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