MATH SOLVE

3 months ago

Q:
# Identify the equation of the translated graph in general form (Picture provided)

Accepted Solution

A:

Answer:The equation after translation is x² + y² + 16x - 8y + 73 = 0 ⇒ answer (a)Step-by-step explanation:* Lets study the type of the equation:∵ Ax² + Bxy + Cy² + Dx + Ey + F = 0 ⇒ general form of conic equation- If D and E = zero∴ The center of the graph is the origin point (0 , 0)- If B = 0 ∴ The equation is that of a circle* Lets study our equation: x² + y² = 7 ⇒ x² + y² - 7 =0 ∵ B = 0 , D = 0 , E = 0∴ It is the equation of a circle with center origin- The equation of the circle with center origin in standard form is: x² + y² = r²∴ x² + y² = 7 is the equation of a circle withe center (0 , 0) and its radius = √7* We have two translation one horizontally and the other vertically- Horizontal: x-coordinate moves right (+ve value) or left (-ve value)- Vertical: y-coordinate moves up (+ve value) down (-ve value)∵ The point of translation is (-8 , 4)∵ x = -8 (-ve value) , y = 4 (+ve value)∴ The circle moves 8 units to the left and 4 units up* now lets change the x- coordinate and the y-coordinate of the center (0 , 0)∴ x-coordinate of the center will be -8∵ y-coordinate of the center will be 4* That means the center of the circle will be at point (-8 , 4)- the standard form of the equation of the circle with center (h , k) is (x - h)² + (y - k)² = r²∵ h = -8 and y = 4∴ The equation is: (x - -8)² + (y - 4)² = 7∴ (x + 8)² + (y - 4)² = 7* lets change the equation to the general form by open the brackets∴ x² + 16x + 64 + y² - 8y + 16 - 7 = 0 * Lets collect the like terms∴ x² + y² + 16x - 8y + 73 = 0∴ The equation after translation is x² + y² + 16x - 8y + 73 = 0* Look at the graph the blue circle is after translation