Change the Cartesian equation x 2 - y 2 = 2 a y into polar (equation) form.

The given Cartesian equation is x 2 - y 2 = 2 a y . . . ( i ) Substitute x = r cos θ , y = r sin θ in eqn. i r 2 cos 2 θ - r 2 sin 2 θ = 2 a r sin θ r 2 cos 2 θ - sin 2 θ = 2 a r sin θ r cos 2 θ = 2 a sin θ Which is the required polar equation.

E M B I B E

The Elements of COORDINATE GEOMETRY Part 1 Cartesian Coordinates>Chapter 1 - Coordinates, Lengths of Straight Lines and Areas of Triangles>EXAMPLES III

S L Loney Solutions for Chapter: Coordinates, Lengths of Straight Lines and Areas of Triangles, Exercise 3: EXAMPLES III

Author:S L Loney

S L Loney Mathematics Solutions for Exercise - S L Loney Solutions for Chapter: Coordinates, Lengths of Straight Lines and Areas of Triangles, Exercise 3: EXAMPLES III

Attempt the practice questions on Chapter 1: Coordinates, Lengths of Straight Lines and Areas of Triangles, Exercise 3: EXAMPLES III with hints and solutions to strengthen your understanding. The Elements of COORDINATE GEOMETRY Part 1 Cartesian Coordinates solutions are prepared by Experienced Embibe Experts.

Questions from S L Loney Solutions for Chapter: Coordinates, Lengths of Straight Lines and Areas of Triangles, Exercise 3: EXAMPLES III with Hints & Solutions

EASY

JEE Advanced

IMPORTANT

The Elements of COORDINATE GEOMETRY Part 1 Cartesian Coordinates>Chapter 1 - Coordinates, Lengths of Straight Lines and Areas of Triangles>EXAMPLES III>Q 18

Find the area of the triangle, the coordinates of whose angular points are $(- a, \frac{π}{6}), (a, \frac{π}{2})$ and $(- 2 a, - \frac{2 π}{3})$ . (where $θ_{3} = \frac{- 2 π}{3}$ )

EASY

JEE Advanced

IMPORTANT

The Elements of COORDINATE GEOMETRY Part 1 Cartesian Coordinates>Chapter 1 - Coordinates, Lengths of Straight Lines and Areas of Triangles>EXAMPLES III>Q 19

Find the polar coordinates (drawing the figure) of the point $x = \sqrt{3}, y = 1$ .

EASY

JEE Advanced

IMPORTANT

The Elements of COORDINATE GEOMETRY Part 1 Cartesian Coordinates>Chapter 1 - Coordinates, Lengths of Straight Lines and Areas of Triangles>EXAMPLES III>Q 25

Change the Cartesian equation $x^{2} + y^{2} = a^{2}$ into polar (equation) form.

EASY

JEE Advanced

IMPORTANT

The Elements of COORDINATE GEOMETRY Part 1 Cartesian Coordinates>Chapter 1 - Coordinates, Lengths of Straight Lines and Areas of Triangles>EXAMPLES III>Q 26

Change the Cartesian equation $y = x \tan α$ in polar(equation) form.

EASY

JEE Advanced

IMPORTANT

The Elements of COORDINATE GEOMETRY Part 1 Cartesian Coordinates>Chapter 1 - Coordinates, Lengths of Straight Lines and Areas of Triangles>EXAMPLES III>Q 27

Change the Cartesian equation $x^{2} + y^{2} = 2 a x$ into polar (equation) form.

EASY

JEE Advanced

IMPORTANT

The Elements of COORDINATE GEOMETRY Part 1 Cartesian Coordinates>Chapter 1 - Coordinates, Lengths of Straight Lines and Areas of Triangles>EXAMPLES III>Q 28

Change the Cartesian equation $= \frac{1}{2} |[(- 2 a^{2}) (\frac{1}{2}) + 2 a^{2} (\frac{1}{2}) - a^{2} (\frac{\sqrt{3}}{2})]|$ into polar (equation) form.

EASY

JEE Advanced

IMPORTANT

The Elements of COORDINATE GEOMETRY Part 1 Cartesian Coordinates>Chapter 1 - Coordinates, Lengths of Straight Lines and Areas of Triangles>EXAMPLES III>Q 30

Change the Cartesian equation ${(x^{2} + y^{2})}^{2} = a^{2} (x^{2} - y^{2})$ into polar (equation) form.