Question Type 3: Converting between different forms Exercises

Convert the Cartesian equation of the line $3x + 4y = 12$ into parametric form $x = x_0 + at$, $y = y_0 + bt$.

Convert the equation $2x - 5y + 10 = 0$ to slope-intercept form $y = mx + c$.

Convert the factorised form $y = (x + 1)(x - 4)$ into standard form $y = ax^2 + bx + c$.

Convert the quadratic $y = 2x^2 - 8x + 5$ into vertex form $y = a(x - h)^2 + k$.

Convert the equation $y = 3x + 7$ to standard form $Ax + By + C = 0$.

Express the equation $9 = 3^x$ in logarithmic form.

Convert the vertex-form quadratic $y = 3(x - 2)^2 + 4$ into standard form $y = ax^2 + bx + c$.

Convert the circle $x^2 + y^2 - 4x + 6y - 12 = 0$ into centre-radius form $(x - h)^2 + (y - k)^2 = r^2$.

Factorise the quadratic $y = x^2 - 6x + 8$ into the form $y = (x - p)(x - q)$.

Express the equation of the circle $(x - 3)^2 + (y + 2)^2 = 25$ in the form $x^2 + y^2 + Dx + Ey + F = 0$.

Convert the parametric line $x = 2t + 1$, $y = -3t + 4$ into a single Cartesian equation in $x$ and $y$.

Express $\log_{2}(16) = x$ in exponential form and find $x$.