Q64.Let the lengths of intercepts on x -axis and y -axis made by the circle x2 + y2 + ax + 2ay + c = 0, (a < 0) be 2√2 and 2√5 , respectively. Then the shortest distance from origin to a tangent to this circle which is perpendicular to the line x + 2y = 0, is equal to : (1) √11 (2) √7 (3) √6 (4) √10
What This Question Tests
The question tests understanding of circle properties including intercepts, finding the equation of a tangent perpendicular to a given line, and calculating the shortest distance from the origin to that tangent.
Concepts Tested
Formulas Used
x-intercept = 2√(g²-c)
y-intercept = 2√(f²-c)
Distance from origin to tangent: |C|/√(A²+B²)
Equation of tangent to circle x²+y²+2gx+2fy+c=0 with slope m: y+f = m(x+g) ± r√(1+m²)
📚 NCERT Sections This Tests
2.1 — Two Charges 5 × 10–8 C And –3 × 10–8 C Are Located 16 Cm Apart. At
Physics Class 11 · Chapter 2
2.1 Two charges 5 × 10–8 C and –3 × 10–8 C are located 16 cm apart. At what point(s) on the line joining the two charges is the electric potential zero? Take the potential at infinity to be zero.
5.11 — Draw All The Isomers (Geometrical And Optical) Of:
Chemistry Class 11 · Chapter 5
5.11 Draw all the isomers (geometrical and optical) of: (i) [CoCl2(en)2] + (ii) [Co(NH3)Cl(en)2] 2+ (iii) [Co(NH3)2Cl2(en)]+
3.10 — In A Reaction Between A And B, The Initial Rate Of Reaction (R0) Was Measured
Chemistry Class 11 · Chapter 3
3.10 In a reaction between A and B, the initial rate of reaction (r0) was measured for different initial concentrations of A and B as given below: A/ mol L–1 0.20 0.20 0.40 B/ mol L–1 0.30 0.10 0.05 r0/mol L–1s–1 5.07 × 10–5 5.07 × 10–5 1.43 × 10–4 What is the order of the reaction with respect to A and B? 3.11 The following results have been obtained during the kinetic studies of the reaction: 2A + B ® C + D Experiment [A]/mol L–1 [B]/mol L–1 Initial rate of formation of D/mol L–1 min–1 I 0.1 0.1 6.0 × 10–3 II 0.3 0.2 7.2 × 10–2 III 0.3 0.4 2.88 × 10–1 IV 0.4 0.1 2.40 × 10–2 Determine the rate law and the rate constant for the reaction. 3.12 The reaction between A and B is first order with respect to A and zero order with respect to B. Fill in the blanks in the following table: Experiment [A]/ mol L–1 [B]/ mol L–1 Initial rate/ mol L–1 min–1 I 0.1 0.1 2.0 × 10–2 II – 0.2 4.0 × 10–2 III 0.4 0.4 – IV – 0.2 2.0 × 10–2 3.13 Calculate the half-life of a first order reaction from their rate constants given below: (i) 200 s–1 (ii) 2 min–1 (iii) 4 years–1 3.14 The half-life for radioactive decay of 14C is 5730 years. An archaeological artifact containing wood had only 80% of the 14C found in a living tree. Estimate the age of the sample. 3.15 The experimental data for decomposition of N2O5 [2N2O5 ® 4NO2 + O2] in gas phase at 318K are given below: t/s 0 400 800 1200 1600 2000 2400 2800 3200 102 × [N2O5]/ 1.63 1.36 1.14 0.93 0.78 0.64 0.53 0.43 0.35 mol L–1 (i) Plot [N2O5] against t. (ii) Find the half-life period for the reaction. (iii) Draw a graph between log[N2O5] and t. (iv) What is the rate law ? Chemistry 86 Reprint 2025-26 (v) Calculate the rate constant. (vi) Calculate the half-life period from k and compare it with (ii).
📋 Question Details
- Chapter
- Circles
- Topic
- Intercepts and tangents of a circle
- Year
- 2021
- Shift
- 16 Mar Shift 2
- Q Number
- Q64
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 11: Conic Sections
More from this Chapter
Q94.Consider a family of circles which are passing through the point (−1, 1) and are tangent to x− axis. If (h, k) are the co-ordinates of the centre of the circles, then the set of values of k is given by the interval (1) 0 < k < 1/2 (2) k ≥1/2 (3) −1/2 ≤k ≤1/2 (4) k ≤1/2
Q79.The point diametrically opposite to the point P(1, 0) on the circle x2 + y2 + 2x + 4y −3 = 0 is (1) (3, −4) (2) (−3, 4) (3) (−3, −4) (4) (3, 4)
Q67.Three distinct points A, B and C are given in the 2 - dimensional coordinate plane such that the ratio of the distance of any one of them from the point (1, 0) to the distance from the point (−1, 0) is equal to 31 . Then the circumcentre of the triangle ABC is at the point JEE Main 2009 JEE Main Previous Year Paper (1) (0, 0) (2) ( 54 , 0) (3) ( 25 , 0) (4) ( 53 , 0)
Q68.If P and Q are the points of intersection of the circles x2 + y2 + 3x + 7y + 2p −5 = 0 and x2 + y2 + 2x + 2y −p2 = 0, then there is a circle passing through P, Q and (1, 1) for (1) all values of p (2) all except one value of p (3) all except two values of p (4) exactly one value of p