Rewrite the equations
1 answer:
You might be interested in
- x² = 16 y
- x = 0
- (x + 4)² = 2/3 (y - 2)
- Gayle identifies that the vertex of the parabola is <u>(3, -1)</u> . The parabola opens <u>right</u>, and the focus is <u>3 </u>units away from the vertex. The directrix is <u>6 </u>units from the focus. The focus is the point <u>(6, -1)</u>. The directrix of the equation is <u>x = 0.</u>
- (y - 6)² = 4p (x - 3)
Step-by-step explanation:
1. First figure
We plot the parabola as given in the attached diagram.
As it is facing upwards, the equation goes as x² = 4py
where, p = 4 (refer the attached diagram)
x² = 4py
x² = 4 (4) y
∴, standard form of parabola is x² = 16 y
2. Second figure
(y + 3)² = 4 (x - 1)
Comparing the given equation with the standard form
(y - k)² = 4p (x - h)
Now from this equation we get to know that
h = 1
p = 1
Directrix is x = (h - p)
So, x = 0
3. Third figure
3x² + 24x - 2y + 52 = 0
3x² + 24x = 2y - 52
3 (x² + 8x) = 2 (y - 26)
(x² + 8x) = 2 (y - 26) / 3
Adding 16 on both sides,
x² + 8x + 16 = 2 (y - 26) / 3 + 16
(x + 4)² = 2/3 y - 52/3 + 16
(x + 4)² = 2/3 y - 4/3
(x + 4)² = 2/3 (y - 2)
4. Fourth figure
(y + 1)² = 12 (x - 3)
Comparing the given equation with the standard form
(y - k)² = 4p (x - h)
Now from this equation we get to know that
k = -1
h = 3
p = 3
Gayle identifies that the vertex of the parabola is <u>(3, -1)</u> . The parabola opens <u>right</u>, and the focus is <u>3 </u>units away from the vertex. The directrix is <u>6 </u>units from the focus. The focus is the point <u>(6, -1)</u>. The directrix of the equation is <u>x = 0.</u>
5. Fifth figure
Focus = (2, 6)
Directrix is x = 4
Therefore, it follows the standard form
(y - k)² = 4p (x - h)
Directrix is given by x = h-p = 4
Focus is given by (h + p, k) = (2, 6)
Solving for (h - p) = 4, (h + p) = 2
2 - p - p = 4
-2p = 2
p = -1
Hence, h = 3
Therefore, the standard form can be written as
(y - 6)² = 4p (x - 3)
Given:
The figure of a rhombus.
To find:
The value of x.
Solution:
We know that, if two lines intersect each other, then the vertically opposite angles are equal.
From the given figure it is clear that the diagonals intersect each other and construct two pairs of vertically opposite angles.
Since and
are vertically opposite angles, therefore
Hence, the value of x is 95°.
We have that the probability of Janice rolling a 2 or 5 on her 7th toss of the dice is
From the question we are told that
Janice rolled either a 2 or a 5 on the last 6 rolls of the die
Janice rolling a 2 or 5 on her 7th toss of the dice
Where
Janice roll the standard die 7th time the probability of getting 2 or 5 is
For more information on this visit
Answer:
Step-by-step explanation: