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Phrases Parabola PYQ

Phrases PYQ
If $x^2 =-16y$ is an equation of parabala then: 

(A) directrix is y = 4 
(B) directrix is x = 4 
(C) co-ordinates of focus are (0,- 4) 
(D) co-ordinates of focus are (-4,-0) 
(E) length of latusrectum =16 

Choose the correct answer from the options given below: 

1. (A) and (E) only 
2. (B), (C) and (E) only 
3. (A), (C) and (E) only 
4. (B), (D) and (E) only





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Phrases Previous Year PYQ Phrases CUET 2025 PYQ

Solution

Given \(x^{2}=-16y\). 
Compare with the standard form \(x^{2}=-4ay\) ⇒ \(4a=16\Rightarrow a=4\). 

Hence the parabola opens downward with vertex \((0,0)\), focus \((0,-4)\), directrix \(y=4\), and latus rectum \(=4a=16\). 
Checking options: 
(A) \(y=4\) ✅, 
(B) \(x=4\) ❌, 
(C) \((0,-4)\) ✅, 
(D) \((-4,0)\) ❌, 
(E) \(16\) ✅. 

Therefore, the correct choice is \(\boxed{3\text{ — (A), (C), and (E) only}}\).
Phrases PYQ
Arrange the parabolas in increasing order of length of their latus rectum. 
(A) $y^2 = 8x$ 
(B) $4x^2 + y = 0$ 
(C) $y^2 - 4y - 3x + 1 = 0$ 
(D) $y^2 - 4y + 4x = 0$

Choose the correct answer:
(a) A, B, C, D
(b) B, C,A, D
(c) C, B, A, D
(d) B, C, D, A






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Phrases Previous Year PYQ Phrases CUET MCA 2026 PYQ

Solution

Phrases PYQ
If a chord which is normal to the parabola $y^2=4ax$ at one end subtends a right angle at the vertex, then its slope is





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Phrases Previous Year PYQ Phrases CUET 2023 PYQ

Solution

For parabola $y^2=4ax$, slope of normal at parameter $t$ is $-t$.
Let slope of chord be $m=-t$.

Since the chord subtends a right angle at the vertex,
$m^2=2$

So,
$m=\sqrt2$
Phrases PYQ
An equilateral triangle is inscribed in a parabola $y^2=8x$ whose one vertix is at the vertex of the parabola then the length of the side of the triangle is:





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Phrases Previous Year PYQ Phrases CUET 2024 PYQ

Solution

Shortcut (Formula):

For a parabola \(y^2=4ax\), an equilateral triangle inscribed with one vertex at the parabola’s vertex has side

\[ s = 8a\sqrt{3}. \]

Here \(y^2=8x \Rightarrow 4a=8 \Rightarrow a=2\). Hence

\[ s = 8\cdot 2\sqrt{3}=16\sqrt{3}. \]

Final Answer: \(16\sqrt{3}\)


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