TS EAMCET · Maths · Parabola
For the parabola \(y=x^2-3 x+2\), match the items in list-1 to that of the items in list-2. S is a focus, Z is intersection of axis and directrix, P is one end point of latus rectum, Q is the point on the parabola at which tangent is parallel to X -axis
| List-1 | List-2 | ||
|---|---|---|---|
| A | P | I | \((2,0)\) |
| B | Q | II | \(\left(\frac{3}{2},-\frac{1}{4}\right)\) |
| C | S | III | \(\left(\frac{3}{2}, 0\right)\) |
| D | Z | IV | \(\left(\frac{3}{2},-\frac{1}{2}\right)\) |
| V | \(\left(0, \frac{3}{2}\right)\) |
- A \(\mathrm{A}-\mathrm{I}, \mathrm{B}-\mathrm{II}, \mathrm{C}-\mathrm{III}, \mathrm{D}-\mathrm{IV}\)
- B \(\mathrm{A}-\mathrm{I}, \mathrm{B}-\mathrm{II}, \mathrm{C}-\mathrm{V}, \mathrm{D}-\mathrm{IV}\)
- C \(\mathrm{A}-\mathrm{II}, \mathrm{B}-\mathrm{V}, \mathrm{C}-\mathrm{III}, \mathrm{D}-\mathrm{IV}\)
- D \(\mathrm{A}-\mathrm{IV}, \mathrm{B}-\mathrm{V}, \mathrm{C}-\mathrm{III}, \mathrm{D}-\mathrm{I}\)
Answer & Solution
Correct Answer
(A) \(\mathrm{A}-\mathrm{I}, \mathrm{B}-\mathrm{II}, \mathrm{C}-\mathrm{III}, \mathrm{D}-\mathrm{IV}\)
Step-by-step Solution
Detailed explanation
\((x-3/2)^2 = y + 1/4 \Rightarrow (x-3/2)^2 = 1(y - (-1/4))\) Vertex \(V = (h, k) = (3/2, -1/4)\), \(4a=1 \Rightarrow a=1/4\) B. Q is the vertex: \(Q = (3/2, -1/4)\). Matches II. C. S (Focus) \( = (h, k+a) = (3/2, -1/4 + 1/4) = (3/2, 0)\). Matches III. D. Directrix…
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