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Standard equations and simple properties of a Parabola
In this Class 11 Mathematics topic from Conic Sections, students study the standard forms of a parabola, such as y² = 4ax and x² = 4ay, and understand how their orientation is represented on the coordinate plane. They identify the vertex, focus, directrix, axis, and length of the latus rectum, while using symmetry and eccentricity to describe basic properties. The topic also develops skill in reading equations, locating key points, and connecting algebraic forms with the corresponding parabola.
Medium · Level 1 · 1 questions
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\((3,0)\)
\((-3,0)\)
\((0,9)\)
\((6,9)\)
Question 1MediumLevel 1
What is the vertex of the parabola represented by \(f(x)=x^2-6x+9\)?फलन \(f(x)=x^2-6x+9\) के ग्राफ पर बने परवलय का शीर्ष कौन-सा है?
Correct answer:सही उत्तर:A
The function can be written as \(f(x)=x^2-6x+9=(x-3)^2\). Comparing it with the standard form \(y=(x-h)^2+k\), we get \(h=3\) and \(k=0\), so the vertex is \((3,0)\). The point \((0,9)\) is the y-intercept, not the vertex. Exam tip: Complete the square to identify the vertex quickly.दिया गया फलन \(f(x)=x^2-6x+9=(x-3)^2\) है। मानक रूप \(y=(x-h)^2+k\) में \(h=3\) और \(k=0\), इसलिए परवलय का शीर्ष \((3,0)\) है। \((0,9)\) शीर्ष नहीं, बल्कि y-अवरोध है। परीक्षा-युक्ति: पूर्ण वर्ग बनाकर शीर्ष सीधे पहचानें।
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