Question

Question 17
Which equation doesn't represent parabola​

Answer 1

Step-by-step explanation:

We know that the general equation of parabola is

y

2

=4ax

y

2

=−4ax

x

2

=4ax

x

2

=−4ax

From option (a),

(x−y)

3

=3

It is not represent the parabola.

From option (b),

y

x

−

x

y

=0

x

2

=y

2

It is not represent the parabola.

From option (c),

y

x

+

x

4

=0

x

2

+4y=0

x

2

=−4y

So, this is represented the parabola.

From option (d),

(x+y)

3

+3=0

It is not represent the parabola.

Hence, option c represents the parabola.

Answer 2

• The parabola is a significant curve of the coordinate geometry's conic sections.
• The fixed point is known as the parabola's focus, and the fixed line is known as the parabola's directrix.  
• It is also worth noting that the fixed point does not lie on the fixed-line.
• A parabola is a locus of any point that is equidistant between a specified point (focus) and a certain line (directrix).
• A parabola's general equation is:

              y = a(x-h)² + k or x = a(y-k)² +h,

                                                       where (h, k) denotes the vertex.

• The standard equation of a regular parabola is y² = 4ax or x²= 4ay

• Example:

1. y² = 8x
2. (y-2)² = 9(x-7)