Home
Class 12
MATHS
Name the conic by finding its standard-f...

Name the conic by finding its standard-form equation.
`2x^(2)+3y^(3)+12x-24y+60=0`

Text Solution

AI Generated Solution

To determine the conic section represented by the equation \(2x^2 + 3y^2 + 12x - 24y + 60 = 0\), we will convert it into its standard form step by step. ### Step 1: Rearrange the equation Start by rearranging the terms to group the \(x\) and \(y\) terms together: \[ 2x^2 + 12x + 3y^2 - 24y + 60 = 0 \] This can be rewritten as: ...
Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

Name the conic by finding its standard-form equation. 4x^(2)+4y^(2)-12x-20y-2=0

What is the center and radius of a circle whose equation is 3x^(2)+3y^(2)-12x+18y=69 ?

Find the angle between the circles given by the equations. x^2 + y^2 - 12x - 6y + 41 = 0, x^2 + y^2 + 4x + 6y - 59 = 0.

The curve represented by the equation 4x^(2)+16y^(2)-24x-24x-32y-12=0 is

it is known that the equation of hyperbola and that of its pair of asymptotes differ by constant . If equation of hyperbola is x^(2) +4xy+3y^(2) -4x+2y+1=0 then find the equation of its pair of asymptoes.

Solve the following system of equations : 2x-3y+13=0;\ \ \ 3x-2y+12=0

Show that the origin is equidistant from the lines 4x + 3y + 10 = 0; 5x - 12y + 26=0 and 7x + 24y = 50.

The equation of the locus of the mid-points of chords of the circle 4x^(2) + 4y^(2) -12x + 4y + 1 = 0 that substend an angle (2pi)/(3) at its centre, is

Find the point at which is shifted such that the transformed equations of the following equations has no first degree term : (i) 2x^(2)+3y^(2)+4x-12y+10=0 (ii) x^(2)+y^(2)-xy-5x+4y+5=0

Find the equation of the circle whose diameter is the common chord of the circles x^(2) + y^(2) + 2x + 3y + 1 = 0 and x^(2) + y^(2) + 4x + 3y + 2 = 0