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Answer: the equation of the standard parabola
1)
The equation of the standard parabola
2) (x+5)^2 = 16(y-2)
Step-by-step explanation:
<u>Explanation </u>
<u>Parabola:-</u>
The set of points in a plane whose distance from a fixed point and a constant ratio to their corresponding perpendicular distance from a fixed straight line is a conic.
Let S be a fixed point and l be a fixed straight line from any point P,the perpendicular PM is drawn to the line 'l'
- The locus of P such that
- The fixed point 'S' is called the Focus.
- The fixed line'l 'is called the directrix of the conic
- The constant ratio is known as the eccentricity, denoted by 'e'
- If e=1 , the conic is called a parabola
1) <u> Step 1</u> :-
Given the focus S = (2,6) and directrix is x=0
we know that
now cross multiplication , we get
squaring on both sides,we get
step 2:-
now using distance formula is
Given S =(2,6) and P(x,y) be any point on parabola
........(1)
Now using perpendicular distance formula
let P(x , y ) be any point on the parabola
Given the directrix is x =0 and P(x,y) be any point on parabola
......(2)
equating equation(1) and equation (2), on simplification
we get .....(3)
- apply
now the equation (3) is
now the standard form of parabola is
<u>Final answer</u>:-
2) <u> Explanation:-</u>
<u>step 1:</u>
Given vertex of a parabola is A(-5,2) and its focus is S(-5,6)
here the given points of 'x'co- ordinates are equal
- Therefore the axis AS is parallel to y- axis
now the standard equation of parabola
now you have to find' a' value
Given vertex of a parabola is A(-5,2) and its focus is S(-5,6)
The distance of
on simplification we get a =4
<u>Final answe</u>r :-
the vertex (h,k) = (-5,2) and a=4
The standard parabola is