CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

The equation of the ellipse whose centre is at the origin and the x-axis, the major axis, which passes through the points (-3, 1) and (2, -2) is


A
5x2+3y2=32
loader
B
3x2+5y2=32
loader
C
5x23y2=32
loader
D
3x2+5y2+32=0
loader

Solution

The correct option is B $$3x^2+5y^2=32$$
Standard equation of ellipse : $$\dfrac { { x }^{ 2 } }{ { a }^{ 2 } } +\dfrac { { y }^{ 2 } }{ { b }^{ 2 } } =1$$
it passes through (-3,1) and (2,-2)
when passing through (-3,1)
                        $$\dfrac { { \left( -3 \right)  }^{ 2 } }{ { a }^{ 2 } } +\dfrac { { (1) }^{ 2 } }{ { b }^{ 2 } } =1$$
                                   $${ 9b }^{ 2 }+{ a }^{ 2 }={ a }^{ 2 }{ b }^{ 2 }\quad \longrightarrow \left( 1 \right) $$
when passing through (2,-2)
                        $$\dfrac { { \left( 2 \right)  }^{ 2 } }{ { a }^{ 2 } } +\dfrac { { \left( -2 \right)  }^{ 2 } }{ { b }^{ 2 } } =1$$
                                 $${ 4a }^{ 2 }+{ 4b }^{ 2 }={ a }^{ 2 }{ b }^{ 2 }\quad \longrightarrow \quad \left( 2 \right) $$
$$eqn(1)=eqn(2)\Rightarrow { 9b }^{ 2 }+{ a }^{ 2 }={ 4a }^{ 2 }+{ 4b }^{ 2 }$$
                                             $$3{ a }^{ 2 }={ 5b }^{ 2 }$$
                                                $${ b }^{ 2 }=\frac { 3 }{ 5 } { a }^{ 2 }\quad \longrightarrow \quad \left( 3 \right) $$
Now, eqn becomes,
                                $$\dfrac { { x }^{ 2 } }{ { a }^{ 2 } } +\dfrac { 5{ y }^{ 2 } }{ { 3a }^{ 2 } } =1$$
                                $$\dfrac { { 3x }^{ 2 }+5{ y }^{ 2 } }{ { 3a }^{ 2 } } =1$$
                                  $${ 3x }^{ 2 }+{ 5y }^{ 2 }={ 3a }^{ 2 }\quad \longrightarrow \quad \left( 4 \right) $$
when passing through (-3,1)
                            $$3\times { \left( -3 \right)  }^{ 2 }+5\times 1=3{ a }^{ 2 }$$
                                                 $$27+5={ 3a }^{ 2 }$$
                                                      $${ 3a }^{ 2 }=32$$$$\quad \longrightarrow \quad \left( 5 \right) $$
putting value of $$3{ a }^{ 2 }$$ in equation(4)
                          $$3{ x }^{ 2 }+{ 5y }^{ 2 }=32$$              Answer

Maths

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
People also searched for
View More



footer-image