Question:
The number of those tangents to the curve $y^2 - 2x^3 - 4y + 8 = 0$ which pass through the point $(1, 2)$ is
The number of those tangents to the curve $y^2 - 2x^3 - 4y + 8 = 0$ which pass through the point $(1, 2)$ is
Show Hint
Set up tangent line equations and solve simultaneous equations for number of tangents through given point.
Updated On: May 19, 2025
- $0$
- $2$
- $1$
- $3$
Hide Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Find the slope of tangent lines to curve at any point
Use point $(1, 2)$ to find tangents passing through it
Result shows exactly 1 tangent passes through $(1, 2)$
Use point $(1, 2)$ to find tangents passing through it
Result shows exactly 1 tangent passes through $(1, 2)$
Was this answer helpful?
0
0
Top Questions on Calculus
- Find the values of \( a \) for which \( f(x) = \sin x - ax + b \) is increasing on \( \mathbb{R} \).
- The number of 6-letter words, with or without meaning, that can be formed using the letters of the word "MATHS" such that any letter that appears in the word must appear at least twice is:
- If \[ f(x) = \int \frac{1}{x^{1/4} (1 + x^{1/4})} \, dx, \quad f(0) = -6, { then } f(1) { is equal to:} \]
- The area of the shaded region (figure) represented by the curves \( y = x^2 \), \( 0 \leq x \leq 2 \), and the y-axis is given by:
- What is the value of \( \int_0^{\pi/2} \sin x \cos x \, dx\)?
View More Questions
Questions Asked in AP EAPCET exam
- The number of all five-letter words (with or without meaning) having at least one repeated letter that can be formed by using the letters of the word INCONVENIENCE is:
- AP EAPCET - 2025
- Binomial Expansion
- If \(\alpha, \beta, \gamma\) are the roots of the equation \[ x^3 - 13x^2 + kx + 189 = 0 \] such that \(\beta - \gamma = 2\), then find the ratio \(\beta + \gamma : k + \alpha\).
- In a container of volume 16.62 m$^3$ at 0°C temperature, 2 moles of oxygen, 5 moles of nitrogen and 3 moles of hydrogen are present, then the pressure in the container is (Universal gas constant = 8.31 J/mol K)
- AP EAPCET - 2025
- Ideal gas equation
- If \[ A = \begin{bmatrix} x & 2 & 1 \\ -2 & y & 0 \\ 2 & 0 & -1 \end{bmatrix}, \] where \( x \) and \( y \) are non-zero real numbers, trace of \( A = 0 \), and determinant of \( A = -6 \), then the minor of the element 1 of \( A \) is:}
- AP EAPCET - 2025
- Complex numbers
- Two objects of masses 5 kg and 10 kg are placed 2 meters apart. What is the gravitational force between them?
(Use \(G = 6.67 \times 10^{-11}\, \mathrm{Nm^2/kg^2}\))- AP EAPCET - 2025
- Gravitation
View More Questions