Exercise 5.3 - Chapter 5 Two Dimensional Analytical Geometry–II 12th Maths Guide Samacheer Kalvi Solutions - SaraNextGen [2024-2025]

Updated On May 15, 2024

By SaraNextGen

Ex $5.3$
Identify the type of conic section for each of the equations.
Question 1.
$
2 \mathrm{x}^2-\mathrm{y}^2=7
$
Solution:
Comparing this equation with the general equation of the conic
$
A x^2+B x y+C y^2+D x+E y+F=0
$
We get $A=2, C=-1$
Elere $\mathrm{A} \neq \mathrm{C}$ also $\mathrm{A}$ and $\mathrm{C}$ are of opposite signs.
So the conic is a hyperbola.
Question 2.
$
3 x^2+3 y^2-4 x+3 y+10=0
$
Sol. Comparing this equation with the general equation of the conic $A x^2+B x y+C y^2+D x+E y+F=0$
We get $A=C$ also $B=0$
So the given conic is a circle.
Question 3.
$
3 \mathrm{x}^2+2 \mathrm{y}^2=14
$
Solution:
Comparing this equation with the general equation of the conic
$
\mathrm{Ax}^2+\mathrm{Bxy}+\mathrm{Cy}^2+\mathrm{Dx}+\mathrm{Ey}+\mathrm{F}=0
$
We get $A \neq C$ also $C$ are of the same sign.
So the given conic is an ellipse.
Question 4.
$
x^2+y^2+x-y=0
$
Solution:
Comparing this equation with the general equation of the conic
$
\mathrm{Ax}^2+\mathrm{Bxy}+\mathrm{Cy}^2+\mathrm{Dx}+\mathrm{Ey}+\mathrm{F}=0
$

We get $A=C$ and $B=0$
So the given conic is a circle.
Question 5.
$
11 x^2-25 y^2-44 x+50 y-256=0
$
Solution:
Comparing this equation with the general equation of the conic
$
A x^2+\mathrm{Bxy}+\mathrm{Cy}{ }^2+\mathrm{Dx}+\mathrm{Ey}+\mathrm{F}=0
$
We get $\mathrm{A} \neq \mathrm{C}$. Also $\mathrm{A}$ and $\mathrm{C}$ are of opposite sign.
So the conic is a hyperbola.
Question 6.
$
y^2+4 x+3 y+4=0
$
Solution:
Comparing this equation with the general equation of the conic $A x^2+B x y+C y^2+D x+E y+F=0$
We get $A=0$ and $B=0$
So the conic is a parabola.

Comparing this equation with the general equation of the conic $A x^2+B x y+C y^2+D x+E y+F=0$
We get $A=0$ and $B=0$
So the conic is a parabola.