List of top Mathematics Questions on Tangents and Normals

The portion of the line $ 4x + 5y = 20 $ in the first quadrant is trisected by the lines $ L_1 $ and $ L_2 $ passing through the origin. The tangent of an angle between the lines $ L_1 $ and $ L_2 $ is:

If A is the area in the first quadrant enclosed by the curve $C: 2x^2 – y + 1 = 0$, the tangent to C at the point (1, 3) and the line x + y = 1, then the value of 60A is ________

If f(x) = e^x, h(x) = (fof) (x), then $\frac{h'(x)}{h'(x)}$ =

Let a curve y = f(x), x ∈ (0, ∞) pass through the points $p ( 1\frac{3 }{2} )$ and Q $ ( a,\frac{1 }{2} )$. If the tangent at any point R(b, f(b)) to the given curve cuts the y-axis at the point S (0, c) such that bc = 3, then (PQ)² is equal to ______.

The tangents at the point $A (1,3)$ and $B (1,-1)$ on the parabola $y^2-2 x-2 y=1$ meet at the point $P$ Then the area (in unit $^2$ ) of $\triangle PAB$ is :-

The number of points on the curve $y=54 x^5-135 x^4-70 x^3+180 x^2+210 x$ at which the normal lines are parallel $to x+90 y+2=0$ is

Let a circle $C_1$ be obtained on rolling the circle $x^2+y^2-4 x-6 y+11=0$ upwards 4 units on the tangent $T$ to it at the point $(3,2)$ Let $C_2$ be the image of $C_1$ in $T$ Let $A$ and $B$ be the centers of circles $C_1$ and $C_2$ respectively, and $M$ and $N$ be respectively the feet of perpendiculars drawn from $A$ and $B$ on the $x$-axis. Then the area of the trapezium AMNB is:

Let a common tangent to the curves y² = 4x and (x – 4)² + y² = 16 touch the curves at the points P and Q. Then (PQ)² is equal to ________.

Let m1 and m2 be the slopes of the tangents drawn from the point P(4,1) to the hyperbola H : $\frac{y^2}{25} − \frac{x^2}{16 }$= 1. If Q is the point from which the tangents drawn to H have slopes |m₁| and |m₂| and they make positive intercepts α and β on the x-axis, then $\frac{( P Q ) ^2}{ α β}$ α β is equal to _____.

A light ray emits from the origin making an angle $30\degree$ with the positive x-axis. After getting reflected by the line $x + y = 1$, if this ray intersects x-axis at Q, then the abscissa of Q is

Let a tangent to the curve $9 x^2+16 y^2=144$ intersect the coordinate axes at the points $A$ and $B$. Then, the minimum length of the line segment $AB$ is

The tangent at point(a cosθ, b sinθ), 0<θ<$\frac{\pi}{2}$, to the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ meets the x-axis at T and y-axis at T₁, Then the value of $\min_{\,\,\,0<\theta<\frac{\pi}{2}}$(OT)(OT₁) is

Angle between tangents to the curve y=x²-5x+6 at the points (2, 0) and (3, 0) is:

The tangent to the curve $x=cost(3-2cos^2t),y=sint(3-2sin^2t)$ at $t=\frac{\pi}{4}$,makes with the $x-axis$ an angle:

The points on the curve $\frac{x^2}{9} + \frac{y^2}{16} = 1$ at which the tangents are parallel to x-axis:

If the tangents at the points P and Q on the circle x² + y²– 2x + y = 5 meet at the point R $( \frac{9}{4},2 ) $then the area of the triangle PQR is

The portion of the tangent to the curve x$^{\frac{2}{3}}$+y$^{\frac{2}{3}}$=a$^{\frac{2}{3}}$, a>0 at any point of it, intercepted between the axes

Let the tangent to the curve x² + 2x – 4y + 9 = 0 at the point P(1, 3) on it meet the y-axis at A. Let the line passing through P and parallel to the line x – 3y = 6 meet the parabola y² = 4x at B. If B lies on the line 2x – 3y = 8. then (AB)² is equal to___

Let the tangent at any point P on a curve passing through the points (1, 1) and ($\frac{1}{10}$,100), intersect positive x-axis and y-axis at the points A and B respectively. If PA : PB = 1 : k and y = y(x) is the solution of the differential equation $\frac{dy}{e^{dx}}Kx+\frac{K}{2}$ , y(0) = k, then 4y(1) – 5log_e3 is equal to ______ .

The area of the region enclosed by the curve y = x³ and its tangent at the point (-1, -1) is

Let the tangent and normal at the point $(3\sqrt{3},1)$ on the ellipse $\frac{ x^2}{36}+\frac{y^2}{4} =1$ meet the y-axis at the points A and B respectively. Let the circle C be drawn taking AB as a diameter and the line x = $2\sqrt{5}$ intersect C at the points P and Q. If the tangents at the points P and Q on the circle intersect at the point (α,β) , then α² - β² is equal to

Consider the plane 2x + y – 3z = 6. If (𝛼, 𝛽, 𝛾) is the image of point (2, 3, 5) in the given plane, then 𝛼 + 𝛽 + 𝛾 = ______

Given below are two statements:
Statement I: The locus of the middle points of chords of the circle x²+ y² = a² which are parallel to the line y=mx is x-my = 0.
Statement II: The two tangents drawn from (4, 2) to x² + y² = 10 are perpendicular.
In the light of the above Statements, choose the most appropriate answer from the options given below :

The number of common tangents that can be drawn to the circle x²+y²-4x-6y-3=0 and x²+y²+2x+2y+1=0 is

The tangent to the hyperbola x²-y² = 3 are parallel to the straight line 2x + y +8=0 points are

List of top Mathematics Questions on Tangents and Normals

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