Question:
If the curve $y=a x^{2}+b x+c, x \in R,$ passes through the point (1,2) and the tangent line to this curve at origin is $y = x ,$ then the possible values of $a , b , c$ are :
If the curve $y=a x^{2}+b x+c, x \in R,$ passes through the point (1,2) and the tangent line to this curve at origin is $y = x ,$ then the possible values of $a , b , c$ are :
Updated On: Feb 14, 2025
- $a =\frac{1}{2}, b =\frac{1}{2}, c =1$
- $a =1, b =0, c =1$
- $a =1, b =1, c =0$
- $a=-1, b=1, c=1$
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The Correct Option is C
Solution and Explanation
$a+b+c=2$...(1)
and $\left.\frac{ dy }{ dx }\right|_{(0,0)}=1$
$2 ax +\left. b \right|_{(0,0)}=1$
$b =1$
Curve passes through origin So,
$c=0$ and $a=1$
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Concepts Used:
Applications of Integrals
There are distinct applications of integrals, out of which some are as follows:
In Maths
Integrals are used to find:
- The center of mass (centroid) of an area having curved sides
- The area between two curves and the area under a curve
- The curve's average value
In Physics
Integrals are used to find:
- Centre of gravity
- Mass and momentum of inertia of vehicles, satellites, and a tower
- The center of mass
- The velocity and the trajectory of a satellite at the time of placing it in orbit
- Thrust