The point `(8,-9)`
with respect to the lines `2x+3y-4=0`
and `6x+9y+8=0`
lies on
the same side of the lines
the different sides of the line
one of the line
none of these
Correct Answer - Both the lines lie on the same side of point (8,-9)
Given lines are parallel lines.
`"Let "L_(1)(x,y) = 2x+3y-4`
`"and "L_(2)(x,y) = 6x+9y+8`
`" " L_(1)(8,-9) =2(8)+3(-9)+4=-7 lt 0`
`" " L_(2)(8,-9) =6(8)+9(-9)+8=-25 lt 0`
Hence, both the lines lie on the same side of point (8,-9).
Correct Answer - c
(1,2,3) satisfies the plane `x-2y+z=0` and also
`(hati+2hatj+3hatk).(hati-2hatj+hatk)=0`
Since the lines `(x-1)/(1)=(y-2)/(2)=(z-3)/(3)and(x)/(1)=(y)/(2)=(z)/(3)`
both satisft (0,0,0) and (1,2,3) both are same. Given line is obviously parallel ot the...
Correct Answer - c
Statement 2 is true as when the line lies in the plane, vector `vecb` along which the line is directed is perpendicular to the normal `vecc` of...
Correct Answer - B
The equation of the line joining the points (2,-1) and (5,-3) is given by
`y+1 = (-1+3)/(2-5)(x-2)`
` "or " 2x+3y-1 = 0 " " (1)`
Since...
Correct Answer - C
Let `P(h,k)` be any point. The chord of contact of P w.r.t. the hyperbola is
`(hx)/(a^(2))-(ky)/(b^(2))=1" (1)"`
The chord of contact of P w.r.t. the auxxiliary circle...
Correct Answer - C
(3) `(sqrt(3h),sqrt(3k+2)+1)^(2)`
`or3h=3k+2+1+2sqrt(3k+2)`
`or3^(2)(h-k-1)^(2)=2^(2)(sqrt(3k+2))^(2)`
`or9(h^(2)+k^(2)+1-2hk-2h+ak)=4(3k+2)`
`or9(x^(2)+y^(2))=18xy-18x+6y+1=0`
Now, `h^(2)=abandDelta!=0`.
Therefore, the locus is a parabola.
Though freezing point and melting point mark same temperature (0°C or 32°F), state of change is different for the two points. At freezing point liquid gets converted into solid, whereas...
