The number of points on the line `3x +4y = 5`, which are at a distance of `sec^(2)theta +2 cossec^(2) theta, theta in R`, from the point (1,3) isA. 1B. 2C. 3D. infinite

The number of points on the line `3x +4y = 5`, which are at a distance

1.	The number of points on the line `3x +4y = 5`, which are at a distance of `sec^(2)theta +2 cossec^(2) theta, theta in R`, from the point (1,3) isA. 1B. 2C. 3D. infinite
Answer» Correct Answer - B The perpendicular distance of (1,3) from the line `3x +4y =5` is 2 units while `sec^(2) theta +2 cosec^(2) theta` `= 3 +(tan theta -sqrt(2) cot theta)^(2) +2sqrt(2)` `ge 3 +2 sqrt(2)`. Evidently, there will be two such points on the line.

The slope of the straight line joining the points `(sqrt(3),1)and(-3,-sqrt(3))` is -A. 1B. `sqrt(3)`C. `(1)/(sqrt(3))`D. `-(1)/(sqrt(3))`
The straight line joining the points (3,-5 ) and (-3,-5) is parallel to the -A. y- axisB. x-axisC. line 3x+5y=0D. line 3x-5y=0
The inclination of the line joining the points `(3-sqrt(3))` and `(sqrt(3),-1)` is -A. `15^(@)`B. `30^(@)`C. `60^(@)`D. `120^(@)`
The straight line joining the points (2,-4) and (2,6) makes an angle of `90^(@)` with the -A. y -axisB. x- axisC. line y=3xD. line x-3y=0
Find the angle between ` x+y=3` and the line joining points (1,1) and (-3,4)A. `tan^(-1)((3)/(7))`B. `pi-tan^(-1)((3)/(7))`C. `tan^(-1)((1)/(7))`D. `pi- tan^(-1)((1)/(7))`
A line meets X-axis in A and Y-axis in B. If R (4,6) is point on the line such that AR:RB=3:2, then the equation of the line isA. y=x+10B. x+y+10=0C. x+y=10D. none of these
The equation of the line having x- intercept =5/3, and perendicular to the join of (5,-2) and (-1,3) isA. 6x-5y=10B. 5x-6y=10C. 6x-5y+10=0D. none of these
The value of k such that the lines `2x-3y+k=0,3x-4y-13=0` and `8x-11y-33=0` are concurrent isA. 7B. -7C. 5D. -5
A line passes through the point `(2,2)` and is perpendicular to the line `3x + y =3,` then its `y`-intercept isA. `(1)/(3)`B. `(2)/(3)`C. 1D. `(4)/(3)`
The slope of the line 3x+2y=8 and its intercept on y- axis is -A. `(-(3)/(2))` and 4 unitsB. `((3)/(2))` and 8 unitsC. `((2)/(3))` and 4 unitsD. `(-(2)/(3))` and 8 units