Question:
If the curve ay $+x^{2}=7$ and $x^{3}=y$ cut orthogonally at $(1,1)$, then a is equal to
A. 1
B. $-6$
C. 6
D. 0
Solution:
Given that the curves $a y+x^{2}=7$ and $x^{3}=y$
Differentiating both of them w.r.t. $x$,
$a \frac{d y}{d x}+2 x=0$ and $3 x^{2}=\frac{d y}{d x}$
$\Rightarrow \frac{d y}{d x}=\frac{-2 x}{a}$ and $\frac{d y}{d x}=3 x^{2}$
For $(1,1)$
$\frac{d y}{d x}=\frac{-2}{a}$ and $\frac{d y}{d x}=3$
Let $\mathrm{m}_{1}=\frac{-2}{a}$ and $\mathrm{m}_{2}=3$
$m_{1} \times m_{2}=-1$
(because curves cut each other orthogonally )
$\Rightarrow \frac{-6}{a}=-1$
$\Rightarrow a=6$
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All Study Material
- JEE Main
- Exam Pattern
- Previous Year Papers
- PYQ Chapterwise
- Physics
- Kinematics 1D
- Kinemetics 2D
- Friction
- Work, Power, Energy
- Centre of Mass and Collision
- Rotational Dynamics
- Gravitation
- Calorimetry
- Elasticity
- Thermal Expansion
- Heat Transfer
- Kinetic Theory of Gases
- Thermodynamics
- Simple Harmonic Motion
- Wave on String
- Sound waves
- Fluid Mechanics
- Electrostatics
- Current Electricity
- Capacitor
- Magnetism and Matter
- Electromagnetic Induction
- Atomic Structure
- Dual Nature of Matter
- Nuclear Physics
- Radioactivity
- Semiconductors
- Communication System
- Error in Measurement & instruments
- Alternating Current
- Electromagnetic Waves
- Wave Optics
- X-Rays
- All Subjects
- Physics
- Motion in a Plane
- Law of Motion
- Work, Energy and Power
- Systems of Particles and Rotational Motion
- Gravitation
- Mechanical Properties of Solids
- Mechanical Properties of Fluids
- Thermal Properties of matter
- Thermodynamics
- Kinetic Theory
- Oscillations
- Waves
- Electric Charge and Fields
- Electrostatic Potential and Capacitance
- Current Electricity
- Thermoelectric Effects of Electric Current
- Heating Effects of Electric Current
- Moving Charges and Magnetism
- Magnetism and Matter
- Electromagnetic Induction
- Alternating Current
- Electromagnetic Wave
- Ray Optics and Optical Instruments
- Wave Optics
- Dual Nature of Radiation and Matter
- Atoms
- Nuclei
- Semiconductor Electronics: Materials, Devices and Simple Circuits.
- Chemical Effects of Electric Current,
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