{"id":294683,"date":"2022-09-10T20:00:02","date_gmt":"2022-09-10T14:30:02","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/question\/if-two-tangents-drawn-from-a-point-p-to-the-parabola-y2-4x-are-at-right-angles-then-the-locus-of-p-is\/"},"modified":"2022-09-10T20:00:02","modified_gmt":"2022-09-10T14:30:02","slug":"if-two-tangents-drawn-from-a-point-p-to-the-parabola-y2-4x-are-at-right-angles-then-the-locus-of-p-is","status":"publish","type":"questions","link":"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/if-two-tangents-drawn-from-a-pointpto-the-parabolay24x\/","title":{"rendered":"If two tangents drawn from a point\u00a0P\u00a0to the parabola\u00a0y2\u00a0=\u00a04x\u00a0are at right angles, then the locus of\u00a0P\u00a0is"},"content":{"rendered":"","protected":false},"author":1,"template":"","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"If two tangents drawn from a point\u00a0P\u00a0to the parabola\u00a0y2\u00a0=\u00a04x\u00a0are at right angles, then the locus of\u00a0P\u00a0is","custom_permalink":"question\/mathematics\/if-two-tangents-drawn-from-a-pointpto-the-parabolay24x\/"},"categories":[],"acf":{"question":"

If two tangents drawn from a point P<\/mi><\/math> to the parabola y<\/mi>2<\/mn> <\/mo><\/mrow><\/msup>=<\/mo> <\/mo>4<\/mn>x<\/mi><\/math> are at right angles, then the locus of <\/mo>P<\/mi><\/math> is<\/p>","options":[{"option":"

 <\/mo>x<\/mi> <\/mo>=<\/mo>\u2013<\/mo> <\/mo>1<\/mn> <\/mo><\/math><\/p>","correct":true},{"option":"

2<\/mn>x<\/mi>-<\/mo> <\/mo>1<\/mn> <\/mo>=<\/mo> <\/mo>0<\/mn><\/math><\/p>","correct":false},{"option":"

 <\/mo>x<\/mi> <\/mo>=<\/mo>1<\/mn><\/math><\/p>","correct":false},{"option":"

2<\/mn>x<\/mi> <\/mo>+<\/mo> <\/mo>1<\/mn> <\/mo>=<\/mo> <\/mo>0<\/mn><\/math><\/p>","correct":false}],"solution":"

Equation of a tangent to the parabola is <\/mo>y<\/mi> <\/mo>=<\/mo> <\/mo>m<\/mi>x<\/mi> <\/mo>+<\/mo> <\/mo>1<\/mn>\/<\/mo>m<\/mi>.<\/mo> <\/mo><\/math>If it passes through <\/mo>P<\/mi>(<\/mo>h<\/mi>,<\/mo> <\/mo>k<\/mi>)<\/mo><\/math>, then<\/p>

 <\/mo>k<\/mi> <\/mo>=<\/mo> <\/mo>m<\/mi>h<\/mi> <\/mo>+<\/mo> <\/mo>1<\/mn>\/<\/mo>m<\/mi><\/math> <\/p>

\u21d2<\/mo>m<\/mi>2<\/mn><\/msup>h<\/mi>\u2212<\/mo>m<\/mi>k<\/mi>+<\/mo>1<\/mn>=<\/mo>0<\/mn><\/math> which gives the slopes of two tangents passing through P. As these are at right angles, product of the s<\/mi>l<\/mi>o<\/mi>p<\/mi>e<\/mi>s<\/mi> <\/mo>=<\/mo>\u2013<\/mo> <\/mo>1<\/mn>\u21d2<\/mo> <\/mo>1<\/mn>\/<\/mo>h<\/mi> <\/mo>=<\/mo> <\/mo>\u2013<\/mo> <\/mo>1<\/mn><\/math> Locus of <\/mo>P<\/mi><\/math> is <\/mo>x<\/mi> <\/mo>=<\/mo>\u2013<\/mo> <\/mo>1<\/mn><\/math> which is the directrix of the parabola.<\/p>","subject":""},"yoast_head":"\nIf two tangents drawn from a point\u00a0P\u00a0to the parabola\u00a0y2\u00a0=\u00a04x\u00a0are at right angles, then the locus of\u00a0P\u00a0is - Infinity Learn by Sri Chaitanya<\/title>\n<meta name=\"description\" content=\"If two tangents drawn from a point\u00a0P\u00a0to the parabola\u00a0y2\u00a0=\u00a04x\u00a0are at right angles, then the locus of\u00a0P\u00a0is\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/if-two-tangents-drawn-from-a-pointpto-the-parabolay24x\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"If two tangents drawn from a point\u00a0P\u00a0to the parabola\u00a0y2\u00a0=\u00a04x\u00a0are at right angles, then the locus of\u00a0P\u00a0is - 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