Question:
The point on the curve $y = \sqrt{x - 1}$ where the tangent is perpendicular to the line $2x + y - 5 = 0 $ is
The point on the curve $y = \sqrt{x - 1}$ where the tangent is perpendicular to the line $2x + y - 5 = 0 $ is
Updated On: May 4, 2024
- (2,-1)
- (10,3)
- (2,1)
- (5,-2)
Hide Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Answer (c) (2,1)
Was this answer helpful?
0
0
Top Questions on Tangents and Normals
- The family of curves whose $x$ and $y$ intercepts of a tangent at any point are respectively double the $x$ and $y$ coordinates of that point is:
- KCET - 2024
- Mathematics
- 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:
- JEE Main - 2024
- Mathematics
- Tangents and Normals
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
- JEE Main - 2023
- Mathematics
- Tangents and Normals
- The number of common tangents, to the circles x² x²+y²-18x-15y+131=0 2 and x2 + y²-6x-6y-7=0, is
- JEE Main - 2023
- Mathematics
- Tangents and Normals
- 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___
- JEE Main - 2023
- Mathematics
- Tangents and Normals
View More Questions
Questions Asked in MHT CET exam
- Total genetic content of an organism is called
- MHT CET - 2024
- Non-Mendelian Genetics
- Two monkeys off mass 10 kg and 8 kg are moving along a vertical light rope the former climbing up with an acceleration of 2 m/second square while the latter coming down with a uniform velocity of 2 m/sec square find the tension in the rope at the fixed support
- MHT CET - 2024
- tension
- Which disease is primarily spread by female Anopheles mosquitoes?
- MHT CET - 2024
- HIV and AIDS
- How many ATP molecules are needed as an initial investment in the glycolytic cycle (normal glycolysis)?
- MHT CET - 2024
- Glycolysis
- If \(A=\begin{bmatrix} 2a & -3b\\ 3 & 2\end{bmatrix}\) and \(\text{adj}A = AA^T\), then 2a+3b is?
- MHT CET - 2023
- Matrices
View More Questions
Concepts Used:
Tangents and Normals
- A tangent at a degree on the curve could be a straight line that touches the curve at that time and whose slope is up to the derivative of the curve at that point. From the definition, you'll be able to deduce the way to realize the equation of the tangent to the curve at any point.
- Given a function y = f(x), the equation of the tangent for this curve at x = x0
- Slope of tangent (at x=x0) m=dy/dx||x=x0
- A normal at a degree on the curve is a line that intersects the curve at that time and is perpendicular to the tangent at that point. If its slope is given by n, and also the slope of the tangent at that point or the value of the derivative at that point is given by m. then we got
m×n = -1
- The normal to a given curve y = f(x) at a point x = x0
- The slope ‘n’ of the normal: As the normal is perpendicular to the tangent, we have: n=-1/m
Diagram Explaining Tangents and Normal:
