Question
Write conic in standard form 4y^2+3x^2=3-x
Answers
GPT 3.5
To write the given conic in standard form, we need to simplify the equation by moving all the terms to one side of the equation.
First, let's expand the equation:
4y^2 + 3x^2 = 3 - x
Rearranging the terms, we get:
4y^2 + 3x^2 + x - 3 = 0
Next, we want to rewrite this equation in standard form, which for a conic section with terms in x and y squared, is given by Ax^2 + By^2 + Cx + Dy + E = 0.
By grouping terms appropriately, the equation simplifies to:
3x^2 + x - 4y^2 - 3 = 0
Therefore, the conic is in standard form:
3x^2 + x - 4y^2 - 3 = 0
First, let's expand the equation:
4y^2 + 3x^2 = 3 - x
Rearranging the terms, we get:
4y^2 + 3x^2 + x - 3 = 0
Next, we want to rewrite this equation in standard form, which for a conic section with terms in x and y squared, is given by Ax^2 + By^2 + Cx + Dy + E = 0.
By grouping terms appropriately, the equation simplifies to:
3x^2 + x - 4y^2 - 3 = 0
Therefore, the conic is in standard form:
3x^2 + x - 4y^2 - 3 = 0