Maths-
General
Easy

Question

P1,P2,P3, be the product of perpendiculars from (0,0) to  x y plus x plus y plus 1 equals 0 comma x squared minus y squared plus 2 x plus 1 equals 0 comma 2 x squared plus 3 x y minus 2 y squared plus 3 x plus y plus 1 equals 0  respectively then:

  1. straight p subscript 1 less than straight p subscript 2 less than straight p subscript 3
  2. straight p subscript 3 less than straight p subscript 2 less than straight p subscript 1
  3. straight p subscript 2 less than straight p subscript 3 less than straight p subscript 1
  4. straight p subscript 1 less than straight p subscript 3 less than straight p subscript 2

hintHint:

use formula for finding the product of perpendicular's for the given lines and then compare them.

The correct answer is: straight p subscript 3 less than straight p subscript 2 less than straight p subscript 1


    Given That:
    P1,P2,P3, be the product of perpendiculars from (0,0) to x y plus x plus y plus 1 equals 0 comma x squared minus y squared plus 2 x plus 1 equals 0 comma 2 x squared plus 3 x y minus 2 y squared plus 3 x plus y plus 1 equals 0   respectively then:
    >>> Product of perpendiculars from (0,0) to x y plus x plus y plus 1 equals 0 is:
    p1 = open vertical bar fraction numerator c over denominator square root of left parenthesis a minus b right parenthesis squared plus 4 h to the power of 2 end exponent end root end fraction close vertical bar
    p1 = 1
    >>> Product of perpendiculars from (0,0) to x squared minus y squared plus 2 x plus 1 equals 0 is:
    p2 = open vertical bar fraction numerator c over denominator square root of left parenthesis a minus b right parenthesis squared plus 4 h to the power of 2 end exponent end root end fraction close vertical bar
    p2 = 1 half
    >>> Product of perpendiculars from (0,0) to 2 x squared plus 3 x y minus 2 y squared plus 3 x plus y plus 1 equals 0:
    p3 = open vertical bar fraction numerator c over denominator square root of left parenthesis a minus b right parenthesis squared plus 4 h to the power of 2 end exponent end root end fraction close vertical bar
    p3 = fraction numerator 1 over denominator square root of 7 end fraction
    >>> Therefore, we can say that straight p subscript 3 less than straight p subscript 2 less than straight p subscript 1.

    P1 = 1;
    P2 = 1 half;
    P3 = fraction numerator 1 over denominator square root of 7 end fraction;
    >>> Therefore, we can say that P1>P2>P3.

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