Slope of a line passing through $\mathrm{P}(2,3)$ and intersecting the line, $x+y=7$ at a distance of 4 units from $\mathrm{P}$, is
$\frac{\sqrt{5}-1}{\sqrt{5}+1}$
$\frac{1-\sqrt{5}}{1+\sqrt{5}}$
$\frac{1-\sqrt{7}}{1+\sqrt{7}}$
$\frac{\sqrt{7}-1}{\sqrt{7}+1}$
Correct Option: , 3
$x=2+r \cos \theta$
$y=3+r \sin \theta$
$\Rightarrow 2+r \cos \theta+3+r \sin \theta=7$
$\Rightarrow r(\cos \theta+\sin \theta)=2$
$\Rightarrow \sin \theta+\cos \theta=\frac{2}{r}=\frac{2}{\pm 4}=\pm \frac{1}{2}$
$\Rightarrow 1+\sin 2 \theta=\frac{1}{4}$
$\Rightarrow \sin 2 \theta=-\frac{3}{4}$
$\Rightarrow \frac{2 m}{1+m^{2}}=-\frac{3}{4}$
$\Rightarrow 3 m^{2}+8 m+3=0$
$\Rightarrow \mathrm{m}=\frac{-4 \pm \sqrt{7}}{1-7}$
$\frac{1-\sqrt{7}}{1+\sqrt{7}}=\frac{(1-\sqrt{7})^{2}}{1-7}=\frac{8-2 \sqrt{7}}{-6}=\frac{-4+\sqrt{7}}{3}$
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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,