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Which of the following equations represents a line perpendicular to \(2x-y+5=0\) and intersecting the \(y\)-axis at \(-3\)?निम्नलिखित में से कौन-सा समीकरण उस रेखा को दर्शाता है जो रेखा \(2x-y+5=0\) के लंबवत है और \(y\)-अक्ष को \(-3\) पर काटती है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(x+2y+6=0\)\(x+2y+6=0\)
Writing the given line as \(y=2x+5\) gives slope \(2\). A perpendicular line has slope \(-\frac12\). With y-intercept \(-3\), it is \(y=-\frac12x-3\), or \(x+2y+6=0\). Exam tip: perpendicular slopes multiply to \(-1\).दी गई रेखा को \(y=2x+5\) लिखने पर उसकी ढाल \(2\) है। लंबवत रेखा की ढाल \(-\frac12\) होगी। \(y\)-अवरोध \(-3\) रखने पर \(y=-\frac12x-3\), अर्थात \(x+2y+6=0\)। परीक्षा में ढालों का गुणनफल \(-1\) जाँचें।
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