If x+√3y = 3 is the tangent to the ellipse 2x2 + 3y2 = k at a point P then the equation of the normal to this ellipse at P is
If x+√3y = 3 is the tangent to the ellipse 2x2 + 3y2 = k at a point P then the equation of the normal to this ellipse at P is
5x - 2√3y = 1
x - √3y = 2
x - √3y + 1 = 0
3x - √3y = 1
The Correct Option is D
Solution and Explanation
The correct option is (D) 3x - √3y = 1
Top Questions on Limits
- Evaluate the following limit :
\(\lim\limits_{x\rightarrow0}\frac{\text{ln}((x^2+1)\cos x)}{x^2}\) = ________. - \(\lim\limits_{x→0} \frac {e^{|2sinx|}-2|sinx|-1}{x^2}\) is
- If the domain of the function \[f(x) = \frac{\sqrt{x^2 - 25}}{(4 - x^2)} + \log_{10}(x^2 + 2x - 15)\]is $(-\infty, \alpha) \cup [\beta, \infty)$, then $\alpha^2 + \beta^3$ is equal to:
- If \[ \alpha = \lim_{x \to 0^+} \left( \frac{e^{\sqrt{\tan x}} - e^{\sqrt{x}}}{\sqrt{\tan x} - \sqrt{x}} \right) \] \[ \beta = \lim_{x \to 0} (1 + \sin x)^{\frac{1}{2\cot x}} \] are the roots of the quadratic equation \(ax^2 + bx - \sqrt{e} = 0\), then \(12 \log_e (a + b)\) is equal to _________.
- If \[ \lim_{x \to 1} \frac{(5x+1)^{1/3} - (x+5)^{1/3}}{(2x+3)^{1/2} - (x+4)^{1/2}} = \frac{m \sqrt{5}}{n (2n)^{2/3}}, \] where \( \text{gcd}(m, n) = 1 \), then \( 8m + 12n \) is equal to _____
Questions Asked in TS EAMCET exam
The ratio of the radii of two solid spheres of same mass in 2:3. The ratio of the moments of inertia of the spheres about their diameters is:
- TS EAMCET - 2023
- rotational motion
If (-c, c) is the set of all values of x for which the expansion is (7 - 5x)-2/3 is valid, then 5c + 7 =
- TS EAMCET - 2023
- Algebra of Complex Numbers
The general solution of the differential equation (x2 + 2)dy +2xydx = ex(x2+2)dx is
- TS EAMCET - 2023
- Differential equations
If i=√-1 then
\[Arg\left[ \frac{(1+i)^{2025}}{1+i^{2022}} \right] =\]- TS EAMCET - 2023
- Trigonometric Identities
If nCr denotes the number of combinations of n distinct things taken r at a time, then the domain of the function g (x)= (16-x)C(2x-1) is
- TS EAMCET - 2023
- permutations and combinations
Concepts Used:
Limits
A function's limit is a number that a function reaches when its independent variable comes to a certain value. The value (say a) to which the function f(x) approaches casually as the independent variable x approaches casually a given value "A" denoted as f(x) = A.
If limx→a- f(x) is the expected value of f when x = a, given the values of ‘f’ near x to the left of ‘a’. This value is also called the left-hand limit of ‘f’ at a.
If limx→a+ f(x) is the expected value of f when x = a, given the values of ‘f’ near x to the right of ‘a’. This value is also called the right-hand limit of f(x) at a.
If the right-hand and left-hand limits concur, then it is referred to as a common value as the limit of f(x) at x = a and denote it by lim x→a f(x).