$
{\text{Write an equation of a horizontal parabola with a vertex of }}\left( { - 1,1} \right){\text{ and a }} \\
{\text{y - intercept of }}\left( {0,2} \right). \\
\\
$
Answer
387.6k+ views
$
{\text{Let the equation of the horizontal parabola is }}{\left( {y - h} \right)^2} = 4a\left( {x - k} \right) \\
{\text{because its y intercept is}}\left( {0,2} \right)\;{\text{which is right side of the parabola }} \\
{\text{i}}{\text{.e parabola is opening right side}}{\text{.}} \\
{\text{so the vertex of the parabola is }}\left( {k,h} \right) \\
{\text{So, compare the vertex from the given vertex}} \\
{\text{i}}{\text{.e }}\left( { - 1,1} \right) \\
\Rightarrow k = - 1,\;h = 1 \\
{\text{So, the equation of parabola is}} \\
{\left( {y - 1} \right)^2} = 4a\left( {x + 1} \right) \\
{\text{Now the y intercept is }}\left( {0,2} \right){\text{ which satisfy the parabola}} \\
\Rightarrow {\left( {2 - 1} \right)^2} = 4a\left( {0 + 1} \right) \\
\Rightarrow 1 = 4a \\
\Rightarrow {\text{Equation of parabola is}} \\
{\left( {y - 1} \right)^2} = x + 1 \\
{\text{So, this is your required equation}}{\text{.}} \\
{\text{NOTE: - In this type of problem first check from given condition parabola is opening which side,}} \\
{\text{ then satisfying the condition according to given problem statement you will get your answer}}{\text{.}} \\
$
{\text{Let the equation of the horizontal parabola is }}{\left( {y - h} \right)^2} = 4a\left( {x - k} \right) \\
{\text{because its y intercept is}}\left( {0,2} \right)\;{\text{which is right side of the parabola }} \\
{\text{i}}{\text{.e parabola is opening right side}}{\text{.}} \\
{\text{so the vertex of the parabola is }}\left( {k,h} \right) \\
{\text{So, compare the vertex from the given vertex}} \\
{\text{i}}{\text{.e }}\left( { - 1,1} \right) \\
\Rightarrow k = - 1,\;h = 1 \\
{\text{So, the equation of parabola is}} \\
{\left( {y - 1} \right)^2} = 4a\left( {x + 1} \right) \\
{\text{Now the y intercept is }}\left( {0,2} \right){\text{ which satisfy the parabola}} \\
\Rightarrow {\left( {2 - 1} \right)^2} = 4a\left( {0 + 1} \right) \\
\Rightarrow 1 = 4a \\
\Rightarrow {\text{Equation of parabola is}} \\
{\left( {y - 1} \right)^2} = x + 1 \\
{\text{So, this is your required equation}}{\text{.}} \\
{\text{NOTE: - In this type of problem first check from given condition parabola is opening which side,}} \\
{\text{ then satisfying the condition according to given problem statement you will get your answer}}{\text{.}} \\
$
Recently Updated Pages
Which of the following would not be a valid reason class 11 biology CBSE

What is meant by monosporic development of female class 11 biology CBSE

Draw labelled diagram of the following i Gram seed class 11 biology CBSE

Explain with the suitable examples the different types class 11 biology CBSE

How is pinnately compound leaf different from palmately class 11 biology CBSE

Match the following Column I Column I A Chlamydomonas class 11 biology CBSE

Trending doubts
Scroll valve is present in a Respiratory system of class 11 biology CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

How fast is 60 miles per hour in kilometres per ho class 10 maths CBSE

How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE

What is the weight in lbs of a 75 Kg person class 11 physics CBSE

Ammocoete larva belongs to A Petromyzon B Myxine C class 11 biology CBSE

State the laws of reflection of light

Use Euclids division algorithm to find the HCF of 570 class 9 maths CBSE

Proton was discovered by A Thomson B Rutherford C Chadwick class 11 chemistry CBSE
