3. Which of the following is the equation of the parabola described with vertex at (5,−3), axis parallel to the y-axis and passing through the point (1,1)?(a) (x−5)2=4(y+3)(b) (x+5)2=4(y−3)(c) (y+3)2=4(x−5)(d) (y−3)2=4(x+5)
Q. 3. Which of the following is the equation of the parabola described with vertex at (5,−3), axis parallel to the y-axis and passing through the point (1,1)?(a) (x−5)2=4(y+3)(b) (x+5)2=4(y−3)(c) (y+3)2=4(x−5)(d) (y−3)2=4(x+5)
Identify general form: Identify the general form of the equation for a parabola with a vertical axis. The standard form is (x−h)2=4p(y−k), where (h,k) is the vertex.
Plug in vertex: Plug in the vertex (5,−3) into the equation. This gives us (x−5)2=4p(y+3).
Use point to find p: Use the point (1,1) to find the value of p. Substitute x=1 and y=1 into the equation: (1−5)2=4p(1+3).
Simplify and solve for p: Simplify and solve for p: 16=4p×4, 16=16p, p=1.
Substitute p back: Substitute p=1 back into the equation: (x−5)2=4(1)(y+3), which simplifies to (x−5)2=4(y+3).
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